T. Blanchard and M. Picco, Frozen into stripes: Fate of the critical Ising model after a quench, Physical Review E, vol.88, issue.3, p.32131, 2013.
DOI : 10.1103/PhysRevE.88.032131

URL : https://hal.archives-ouvertes.fr/hal-00818107

T. Blanchard, Wrapping probabilities for Ising spin clusters on a torus, Journal of Physics A: Mathematical and Theoretical, vol.47, issue.34, p.342002, 2014.
DOI : 10.1088/1751-8113/47/34/342002

T. Blanchard, F. Corberi, L. F. Cugliandolo, and M. Picco, How soon after a zero-temperature quench is the fate of the Ising model sealed?, EPL (Europhysics Letters), vol.106, issue.6, p.66001, 2014.
DOI : 10.1209/0295-5075/106/66001

URL : https://hal.archives-ouvertes.fr/hal-00933708

S. R. Broadbent and J. M. Hammersley, Percolation processes, Mathematical Proceedings of the Cambridge Philosophical Society, vol.16, issue.03, pp.629-641
DOI : 10.1017/S0305004100032680

D. Stauffer and A. Aharony, Introduction to percolation theory, 1994.
DOI : 10.1063/1.2820231

Z. Martin and . Bazant, Largest cluster in subcritical percolation, Phys. Rev. E, vol.62, issue.2, pp.1660-1669, 2000.

R. Van, D. Hofstad, and F. Redig, Maximal clusters in non-critical percolation and related models, J Stat Phys, vol.122, issue.4, pp.671-703, 2006.

F. Y. Wu, The Potts model, Reviews of Modern Physics, vol.54, issue.1, p.235, 1982.
DOI : 10.1103/RevModPhys.54.235

G. R. Grimmett, The Random-Cluster Model, 2006.

C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model, Physica, vol.57, issue.4, p.536, 1972.
DOI : 10.1016/0031-8914(72)90045-6

C. M. Fortuin, On the random-cluster model II. The percolation model, Physica, vol.58, issue.3, pp.393-418, 1972.
DOI : 10.1016/0031-8914(72)90161-9

C. M. Fortuin, On the random-cluster model, Physica, vol.59, issue.4, pp.545-570, 1972.
DOI : 10.1016/0031-8914(72)90087-0

J. L. Cardy, Critical percolation in finite geometries, Journal of Physics A: Mathematical and General, vol.25, issue.4, pp.201-206, 1992.
DOI : 10.1088/0305-4470/25/4/009

A. J. Bray, Theory of phase-ordering kinetics Advances in Physics, pp.357-459, 1994.

M. Henkel and M. Pleimling, Non-Equilibrium Phase Transitions Ageing and Dynamical Scaling Far from Equilibrium, 2011.

L. John and . Cardy, Scaling and Renormalization in Statistical Physics, 1996.

J. Daniel, V. Amit, and . Martin-mayor, Field Theory, the Renormalization Group, And Critical Phenomena: Graphs To Computers, 2005.

P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Reviews of Modern Physics, vol.49, issue.3, p.435, 1977.
DOI : 10.1103/RevModPhys.49.435

A. Picone and M. Henkel, Response of non-equilibrium systems with long-range initial correlations, Journal of Physics A: Mathematical and General, vol.35, issue.27, p.5575, 2002.
DOI : 10.1088/0305-4470/35/27/304

URL : https://hal.archives-ouvertes.fr/hal-00132020

A. Picone and M. Henkel, Local scale-invariance and ageing in noisy systems, Nuclear Physics B, vol.688, issue.3, pp.217-265, 2004.
DOI : 10.1016/j.nuclphysb.2004.03.028

URL : https://hal.archives-ouvertes.fr/hal-00132139

B. Sreedhar and . Dutta, The role of initial conditions in the ageing of the long-range spherical model, J. Phys. A: Math. Theor, vol.41, issue.39, p.395002, 2008.

.. Scaling-of-cluster-quantities, 35 1.2.1 A few hints on conformal field theory, 37 1.2.3 Dynamical scaling of distributions . . . . . . . . . . . . . . . . . . . . . . . . . 38

T. Blanchard, L. F. Cugliandolo, and M. Picco, A morphological study of cluster dynamics between critical points, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.05, pp.2012-05026, 2012.
DOI : 10.1088/1742-5468/2012/05/P05026

URL : https://hal.archives-ouvertes.fr/hal-00683575

P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Reviews of Modern Physics, vol.49, issue.3, p.435, 1977.
DOI : 10.1103/RevModPhys.49.435

H. K. Janssen, From Phase Transitions to Chaos?Topics in Modern Statistical Physics, page 68, World Scientific, 1992.

P. Calabrese and A. Gambassi, Ageing properties of critical systems, Journal of Physics A: Mathematical and General, vol.38, issue.18, p.133, 2005.
DOI : 10.1088/0305-4470/38/18/R01

U. C. Täuber, Critical dynamics -A field theory approach to equilibrium and nonequilibrium scaling behavior

B. Nienhuis, Coulomb gas formulation of two dimensional phase transitions, Phase Transitions and Critical Phenomena, vol.11, p.1, 1987.

J. Cardy, SLE for theoretical physicists, Annals of Physics, vol.318, issue.1, p.81, 2005.
DOI : 10.1016/j.aop.2005.04.001

A. Ilya and . Gruzberg, Stochastic geometry of critical curves, Schramm?Loewner evolutions and conformal field theory, J. Phys. A: Math. Gen, vol.39, issue.41, p.12601, 2006.

J. Jeferson, A. J. Arenzon, L. F. Bray, A. Cugliandolo, and . Sicilia, Exact Results for Curvature-Driven Coarsening in Two Dimensions, Phys. Rev. Lett, issue.14, p.988, 2007.

A. Sicilia, J. J. Arenzon, A. J. Bray, and L. F. Cugliandolo, Domain growth morphology in curvature-driven two-dimensional coarsening, Physical Review E, vol.76, issue.6, p.76061116, 2007.
DOI : 10.1103/PhysRevE.76.061116

URL : https://hal.archives-ouvertes.fr/hal-00170288

K. Barros, P. L. Krapivsky, and R. S. , Freezing into stripe states in two-dimensional ferromagnets and crossing probabilities in critical percolation, Physical Review E, vol.80, issue.4, p.40101, 2009.
DOI : 10.1103/PhysRevE.80.040101

A. Sicilia, Y. Sarrazin, J. J. Arenzon, A. J. Bray, and L. F. Cugliandolo, Geometry of phase separation, Physical Review E, vol.80, issue.3, p.31121, 2009.
DOI : 10.1103/PhysRevE.80.031121

URL : https://hal.archives-ouvertes.fr/hal-00519911

A. Sicilia, J. J. Arenzon, A. J. Bray, and L. F. Cugliandolo, Geometric properties of two-dimensional coarsening with weak disorder, EPL (Europhysics Letters), vol.82, issue.1, p.10001, 2008.
DOI : 10.1209/0295-5075/82/10001

URL : https://hal.archives-ouvertes.fr/hal-00519898

M. P. Loureiro, J. J. Arenzon, L. F. Cugliandolo, and A. Sicilia, Curvature-driven coarsening in the two-dimensional Potts model, Physical Review E, vol.81, issue.2, p.21129, 2010.
DOI : 10.1103/PhysRevE.81.021129

URL : https://hal.archives-ouvertes.fr/hal-00519924

M. P. Loureiro, J. J. Arenzon, and L. F. Cugliandolo, Geometrical properties of the Potts model during the coarsening regime, Physical Review E, vol.85, issue.2, p.21135, 2012.
DOI : 10.1103/PhysRevE.85.021135

M. Sykes and D. Gaunt, A note on the mean size of clusters in the Ising model, Journal of Physics A: Mathematical and General, vol.9, issue.12, p.2131, 1976.
DOI : 10.1088/0305-4470/9/12/017

A. Coniglio and W. Klein, Clusters and Ising critical droplets: a renormalisation group approach, Journal of Physics A: Mathematical and General, vol.13, issue.8, p.2775, 1980.
DOI : 10.1088/0305-4470/13/8/025

B. Duplantier, Conformally Invariant Fractals and Potential Theory, Physical Review Letters, vol.84, issue.7, p.1363, 2000.
DOI : 10.1103/PhysRevLett.84.1363

URL : https://hal.archives-ouvertes.fr/hal-00087400

W. Janke, M. J. Adriaan, and . Schakel, Geometrical vs. Fortuin???Kasteleyn clusters in the two-dimensional q-state Potts model, Nuclear Physics B, vol.700, issue.1-3, pp.1-3385, 2004.
DOI : 10.1016/j.nuclphysb.2004.08.030

A. L. Stella and C. Vanderzande, critical point, Physical Review Letters, vol.62, issue.10, p.1067, 1989.
DOI : 10.1103/PhysRevLett.62.1067

B. Duplantier and H. Saleur, Exact fractal dimension of 2D Ising clusters, Physical Review Letters, vol.63, issue.22, p.2536, 1989.
DOI : 10.1103/PhysRevLett.63.2536

M. Picco, A. Santachiara, and . Sicilia, Geometrical properties of parafermionic spin models, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.04, p.4013, 2009.
DOI : 10.1088/1742-5468/2009/04/P04013

URL : https://hal.archives-ouvertes.fr/hal-00348289

H. Müller-krumbhaar, Percolation in a lattice system with particle interaction, Physics Letters A, vol.50, issue.1, p.27, 1974.
DOI : 10.1016/0375-9601(74)90337-5

J. Jeferson, A. J. Arenzon, L. F. Bray, A. Cugliandolo, and . Sicilia, Exact results for curvature-driven coarsening in two dimensions, Phy. Rev. Lett, issue.14, p.98145701, 2007.

A. Sicilia, J. J. Arenzon, I. Dierking, A. J. Bray, L. F. Cugliandolo et al., Experimental Test of Curvature-Driven Dynamics in the Phase Ordering of a Two Dimensional Liquid Crystal, Physical Review Letters, vol.101, issue.19, 2008.
DOI : 10.1103/PhysRevLett.101.197801

URL : https://hal.archives-ouvertes.fr/hal-00519909

J. Cardy and R. Ziff, Exact results for the universal area distribution of clusters in percolation, Ising, and Potts models, J. Stat. Phys, vol.110, issue.1, 2003.

M. F. Sykes and J. W. Essam, Some Exact Critical Percolation Probabilities for Bond and Site Problems in Two Dimensions, Physical Review Letters, vol.10, issue.1, p.3, 1963.
DOI : 10.1103/PhysRevLett.10.3

R. Bausch, H. K. Janssen, and H. Wagner, Renormalized field theory of critical dynamics, Zeitschrift f???r Physik B Condensed Matter and Quanta, vol.33, issue.1, p.113, 1976.
DOI : 10.1007/BF01312880

M. P. Nightingale and H. W. Blöte, Monte Carlo computation of correlation times of independent relaxation modes at criticality, Physical Review B, vol.62, issue.2, p.1089, 2000.
DOI : 10.1103/PhysRevB.62.1089

S. Smirnov, Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.3, p.239, 2001.
DOI : 10.1016/S0764-4442(01)01991-7

S. Smirnov, Towards conformal invariance of 2D lattice models, Proc. Int. Congr. Math, vol.2, p.1421, 2006.
DOI : 10.4171/022-2/68

D. Chelkak and S. Smirnov, Universality in the 2D Ising model and conformal invariance of fermionic observables, Inventiones mathematicae, vol.172, issue.3, 2009.
DOI : 10.1007/s00222-011-0371-2

B. Duplantier and H. Saleur, Winding-Angle Distributions of Two-Dimensional Self-Avoiding Walks from Conformal Invariance, Physical Review Letters, vol.60, issue.23, p.2343, 1988.
DOI : 10.1103/PhysRevLett.60.2343

B. Duplantier and I. A. Binder, Harmonic Measure and Winding of Conformally Invariant Curves, Physical Review Letters, vol.89, issue.26, p.264101, 2002.
DOI : 10.1103/PhysRevLett.89.264101

B. Wieland and D. B. Wilson, Winding angle variance of Fortuin-Kasteleyn contours, Physical Review E, vol.68, issue.5, p.56101, 2003.
DOI : 10.1103/PhysRevE.68.056101

W. Klein, H. E. Stanley, P. J. Reynolds, and A. Coniglio, Renormalization-Group Approach to the Percolation Properties of the Triangular Ising Model, Physical Review Letters, vol.41, issue.17, p.411145, 1978.
DOI : 10.1103/PhysRevLett.41.1145

A. Balint, F. Camia, and R. Meester, The High Temperature Ising Model on the Triangular Lattice is a Critical Bernoulli Percolation Model, Journal of Statistical Physics, vol.26, issue.1, p.122, 2010.
DOI : 10.1007/s10955-010-9930-y

M. Bauer, J. Bernard, and . Houdayer, Dipolar stochastic Loewner evolutions, Journal of Statistical Mechanics: Theory and Experiment, vol.2005, issue.03, p.3001, 2005.
DOI : 10.1088/1742-5468/2005/03/P03001

A. Sicilia, J. Jeferson, A. J. Arenzon, L. F. Bray, and . Cugliandolo, Domain growth morphology in curvature driven two dimensional coarsening. 0706, Phys. Rev. E, vol.4314, issue.76, p.61116, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00170288

K. Barros, P. L. Krapivsky, and S. Redner, Freezing into stripe states in two-dimensional ferromagnets and crossing probabilities in critical percolation, Physical Review E, vol.80, issue.4, p.40101, 2009.
DOI : 10.1103/PhysRevE.80.040101

J. Olejarz, P. L. Krapivsky, and S. Redner, Fate of 2D Kinetic Ferromagnets and Critical Percolation Crossing Probabilities, Physical Review Letters, vol.109, issue.19, p.195702, 2012.
DOI : 10.1103/PhysRevLett.109.195702

J. L. Cardy, Critical percolation in finite geometries, Journal of Physics A: Mathematical and General, vol.25, issue.4, pp.201-206, 1992.
DOI : 10.1088/0305-4470/25/4/009

T. Haru and . Pinson, Critical percolation on the torus, J. Stat. Phys, vol.75, issue.5-6, pp.1167-1177, 1994.

G. M. Watts, A crossing probability for critical percolation in two dimensions, Journal of Physics A: Mathematical and General, vol.29, issue.14, p.363, 1996.
DOI : 10.1088/0305-4470/29/14/002

J. Cardy, Crossing formulae for critical percolation in an annulus, Journal of Physics A: Mathematical and General, vol.35, issue.41, pp.565-572, 2002.
DOI : 10.1088/0305-4470/35/41/102

E. Lapalme and Y. Saint-aubin, Crossing probabilities on same-spin clusters in the two-dimensional Ising model, Journal of Physics A: Mathematical and General, vol.34, issue.9, pp.1825-1835, 2001.
DOI : 10.1088/0305-4470/34/9/302

L. Arguin and Y. Saint-aubin, Non-unitary observables in the 2d critical Ising model, Physics Letters B, vol.541, issue.3-4, pp.384-389, 2002.
DOI : 10.1016/S0370-2693(02)02228-1

M. Bauer, D. Bernard, and K. Kytölä, Multiple Schramm???Loewner Evolutions and Statistical Mechanics Martingales, Journal of Statistical Physics, vol.557, issue.3, pp.5-61125, 2005.
DOI : 10.1007/s10955-005-7002-5

URL : https://hal.archives-ouvertes.fr/hal-00023298

J. Michael and . Kozdron, Using the Schramm?Loewner evolution to explain certain non-local observables in the 2D critical Ising model, J. Phys. A: Math. Theo, vol.42, issue.26, p.265003, 2009.

J. Dubail, J. L. Jacobsen, and H. Saleur, Conformal boundary conditions in the critical model and dilute loop models, Nuclear Physics B, vol.827, issue.3, pp.457-502, 2010.
DOI : 10.1016/j.nuclphysb.2009.10.016

URL : https://hal.archives-ouvertes.fr/hal-00382588

O. Schramm, Scaling limits of loop-erased random walks and uniform spanning trees, Israel Journal of Mathematics, vol.111, issue.1, pp.221-288, 2000.
DOI : 10.1007/BF02803524

S. Smirnov, Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.3, p.239, 2001.
DOI : 10.1016/S0764-4442(01)01991-7

E. Lapalme and Y. Saint-aubin, Crossing probabilities on same-spin clusters in the two-dimensional Ising model, Journal of Physics A: Mathematical and General, vol.34, issue.9, pp.1825-1835, 2001.
DOI : 10.1088/0305-4470/34/9/302

U. Wolff, Collective Monte Carlo Updating for Spin Systems, Physical Review Letters, vol.62, issue.4, p.361, 1989.
DOI : 10.1103/PhysRevLett.62.361

A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, A new algorithm for Monte Carlo simulation of Ising spin systems, Journal of Computational Physics, vol.17, issue.1, pp.10-18, 1975.
DOI : 10.1016/0021-9991(75)90060-1

L. Arguin, Homology of Fortuin-Kasteleyn clusters of Potts models on the torus, Journal of Statistical Physics, vol.109, issue.1/2, pp.301-310, 2002.
DOI : 10.1023/A:1019979326380

A. L. Stella and C. Vanderzande, critical point, Physical Review Letters, vol.62, issue.10, p.1067, 1989.
DOI : 10.1103/PhysRevLett.62.1067

T. Blanchard, Wrapping probabilities for Ising spin clusters on a torus, Journal of Physics A: Mathematical and Theoretical, vol.47, issue.34, p.342002, 2014.
DOI : 10.1088/1751-8113/47/34/342002

A. J. Bray, K. Humayun, and T. J. Newman, Kinetics of ordering for correlated initial conditions, Physical Review B, vol.43, issue.4, pp.3699-3702, 1991.
DOI : 10.1103/PhysRevB.43.3699

B. Derrida, Dynamical phase transition in nonsymmetric spin glasses, Journal of Physics A: Mathematical and General, vol.20, issue.11, p.721, 1987.
DOI : 10.1088/0305-4470/20/11/009

L. F. Cugliandolo and D. S. Dean, Full dynamical solution for a spherical spin-glass model, Journal of Physics A: Mathematical and General, vol.28, issue.15, p.4213, 1995.
DOI : 10.1088/0305-4470/28/15/003

A. Barrat, R. Burioni, and M. Mézard, Ageing classification in glassy dynamics, Journal of Physics A: Mathematical and General, vol.29, issue.7, p.1311, 1996.
DOI : 10.1088/0305-4470/29/7/005

J. Ye, J. Machta, C. M. Newman, and D. L. Stein, Nature versus nurture: Predictability in low-temperature Ising dynamics, Physical Review E, vol.88, issue.4, p.40101, 2013.
DOI : 10.1103/PhysRevE.88.040101

A. J. Bray, N. Satya, G. Majumdar, and . Schehr, Persistence and first-passage properties in nonequilibrium systems, Advances in Physics, vol.87, issue.2, pp.225-361, 2013.
DOI : 10.1038/nature06201

URL : https://hal.archives-ouvertes.fr/hal-00843539

A. J. Bray, B. Derrida, and C. Godréche, Non-Trivial Algebraic Decay in a Soluble Model of Coarsening, Europhysics Letters (EPL), vol.27, issue.3, p.175, 1994.
DOI : 10.1209/0295-5075/27/3/001

B. Derrida, A. J. Bray, and C. Godreche, Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models, Journal of Physics A: Mathematical and General, vol.27, issue.11, p.357, 1994.
DOI : 10.1088/0305-4470/27/11/002

URL : https://hal.archives-ouvertes.fr/hal-00165918

D. Stauffer, Ising spinodal decomposition at T=O in one to five dimensions, Journal of Physics A: Mathematical and General, vol.27, issue.14, p.5029, 1994.
DOI : 10.1088/0305-4470/27/14/027

B. Derrida, V. Hakim, and V. Pasquier, Exact First-Passage Exponents of 1D Domain Growth: Relation to a Reaction-Diffusion Model, Physical Review Letters, vol.75, issue.4, pp.751-754, 1995.
DOI : 10.1103/PhysRevLett.75.751

B. Derrida, V. Hakim, and V. Pasquier, Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model, Journal of Statistical Physics, vol.28, issue.5-6, pp.5-6763, 1996.
DOI : 10.1007/BF02199362

N. Satya, C. Majumdar, and . Sire, Survival probability of a gaussian nonmarkovian process: Application to the T=0 dynamics of the Ising model, Phys. Rev. Lett, vol.77, issue.8, pp.1420-1423, 1996.

C. Sire, N. Satya, A. Majumdar, and . Rüdinger, Analytical results for random walk persistence, Physical Review E, vol.61, issue.2, pp.1258-1269, 2000.
DOI : 10.1103/PhysRevE.61.1258

URL : https://hal.archives-ouvertes.fr/hal-00004866

B. Yurke, A. N. Pargellis, S. N. Majumdar, and C. Sire, Experimental measurement of the persistence exponent of the planar Ising model, Physical Review E, vol.56, issue.1, pp.40-42, 1997.
DOI : 10.1103/PhysRevE.56.R40

URL : https://hal.archives-ouvertes.fr/hal-00004858

G. Manoj and P. Ray, Scaling and fractal formation in persistence, Journal of Physics A: Mathematical and General, vol.33, issue.12, p.109, 2000.
DOI : 10.1088/0305-4470/33/12/103

G. Manoj and P. Ray, Spatial distribution of persistent sites, Journal of Physics A: Mathematical and General, vol.33, issue.31, p.5489, 2000.
DOI : 10.1088/0305-4470/33/31/304

S. Jain and H. Flynn, Scaling and persistence in the two-dimensional Ising model, Journal of Physics A: Mathematical and General, vol.33, issue.47, p.8383, 2000.
DOI : 10.1088/0305-4470/33/47/305

G. Manoj and P. Ray, Persistence in higher dimensions: A finite size scaling study, Physical Review E, vol.62, issue.6, pp.7755-7758, 2000.
DOI : 10.1103/PhysRevE.62.7755

P. Ray, Persistence in Extended Dynamical Systems, Phase Transitions, vol.85, issue.5-7, pp.563-579, 2004.
DOI : 10.1103/PhysRevLett.56.2553

A. J. Bray, Theory of phase-ordering kinetics Advances in Physics, pp.357-459, 1994.

J. Olejarz, P. L. Krapivsky, and S. Redner, Zero-temperature freezing in the three-dimensional kinetic Ising model, Physical Review E, vol.83, issue.3, p.30104, 2011.
DOI : 10.1103/PhysRevE.83.030104

J. Olejarz, P. L. Krapivsky, and S. Redner, Zero-temperature relaxation of three-dimensional Ising ferromagnets, Physical Review E, vol.83, issue.5, p.51104, 2011.
DOI : 10.1103/PhysRevE.83.051104

H. Takano and S. Miyashita, Ordering process in the kinetic Ising model on the honeycomb lattice, Physical Review B, vol.48, issue.10, p.7221, 1993.
DOI : 10.1103/PhysRevB.48.7221

T. Blanchard, F. Corberi, L. F. Cugliandolo, and M. Picco, How soon after a zero-temperature quench is the fate of the Ising model sealed?, EPL (Europhysics Letters), vol.106, issue.6, p.66001, 2014.
DOI : 10.1209/0295-5075/106/66001

URL : https://hal.archives-ouvertes.fr/hal-00933708

J. Cardy and R. Ziff, Exact results for the universal area distribution of clusters in percolation, Ising, and Potts models, J. Stat. Phys, vol.110, issue.1, 2003.

A. Barrat, Monte Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes, Physical Review E, vol.57, issue.3, pp.3629-3632, 1998.
DOI : 10.1103/PhysRevE.57.3629

F. Corberi, E. Lippiello, A. Sarracino, and M. Zannetti, Fluctuations of two-time quantities and non-linear response functions, Journal of Statistical Mechanics: Theory and Experiment, vol.2010, issue.04, p.4003, 2010.
DOI : 10.1088/1742-5468/2010/04/P04003

S. Jain, Zero-temperature dynamics of the weakly disordered Ising model, Physical Review E, vol.59, issue.3, pp.2493-2496, 1999.
DOI : 10.1103/PhysRevE.59.R2493

H. E. Stanley, Cluster shapes at the percolation threshold: and effective cluster dimensionality and its connection with critical-point exponents, Journal of Physics A: Mathematical and General, vol.10, issue.11, p.211, 1977.
DOI : 10.1088/0305-4470/10/11/008

R. Pike and H. E. Stanley, Order propagation near the percolation threshold, Journal of Physics A: Mathematical and General, vol.14, issue.5, p.169, 1981.
DOI : 10.1088/0305-4470/14/5/013

A. Coniglio, -Vector Models at the Percolation Threshold, Physical Review Letters, vol.46, issue.4, pp.250-253, 1981.
DOI : 10.1103/PhysRevLett.46.250

URL : https://hal.archives-ouvertes.fr/hal-01080271

A. Coniglio, Fractal structure of Ising and Potts clusters: Exact results, Physical Review Letters, vol.62, issue.26, pp.3054-3057, 1989.
DOI : 10.1103/PhysRevLett.62.3054

G. Provencher, Y. Saint-aubin, P. A. Pearce, and J. Rasmussen, Geometric Exponents of Dilute Loop Models, Journal of Statistical Physics, vol.21, issue.2, pp.315-350, 2012.
DOI : 10.1007/s10955-012-0464-3

A. Sicilia, J. J. Arenzon, I. Dierking, A. J. Bray, L. F. Cugliandolo et al., Experimental Test of Curvature-Driven Dynamics in the Phase Ordering of a Two Dimensional Liquid Crystal, Physical Review Letters, vol.101, issue.19, 2008.
DOI : 10.1103/PhysRevLett.101.197801

URL : https://hal.archives-ouvertes.fr/hal-00519909

D. Bouttes, E. Gouillart, E. Boller, D. Dalmas, and D. Vandembroucq, X-Ray Tomographic Study, Physical Review Letters, vol.112, issue.24, p.245701, 2014.
DOI : 10.1103/PhysRevLett.112.245701

URL : https://hal.archives-ouvertes.fr/hal-01058261

T. Blanchard, Wrapping probabilities for Ising spin clusters on a torus, Journal of Physics A: Mathematical and Theoretical, vol.47, issue.34, p.342002, 2014.
DOI : 10.1088/1751-8113/47/34/342002

C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model, Physica, vol.57, issue.4, p.536, 1972.
DOI : 10.1016/0031-8914(72)90045-6

A. Coniglio and W. Klein, Clusters and Ising critical droplets: a renormalisation group approach, Journal of Physics A: Mathematical and General, vol.13, issue.8, p.2775, 1980.
DOI : 10.1088/0305-4470/13/8/025

W. Janke, M. J. Adriaan, and . Schakel, Geometrical vs. Fortuin???Kasteleyn clusters in the two-dimensional q-state Potts model, Nuclear Physics B, vol.700, issue.1-3, pp.1-3385, 2004.
DOI : 10.1016/j.nuclphysb.2004.08.030

W. Janke and A. M. Schakel, Fractal structure of spin clusters and domain walls in the two-dimensional Ising model, Physical Review E, vol.71, issue.3, p.71036703, 2005.
DOI : 10.1103/PhysRevE.71.036703

A. L. Stella and C. Vanderzande, critical point, Physical Review Letters, vol.62, issue.10, p.1067, 1989.
DOI : 10.1103/PhysRevLett.62.1067

A. Coniglio and F. Peruggi, Clusters and droplets in the q-state Potts model, Journal of Physics A: Mathematical and General, vol.15, issue.6, p.1873, 1982.
DOI : 10.1088/0305-4470/15/6/028

C. Vanderzande, Fractal dimensions of Potts clusters, Journal of Physics A: Mathematical and General, vol.25, issue.2, p.75, 1992.
DOI : 10.1088/0305-4470/25/2/008

F. Y. Wu, The Potts model, Reviews of Modern Physics, vol.54, issue.1, p.235, 1982.
DOI : 10.1103/RevModPhys.54.235

Y. Deng, W. J. Henk, B. Blöte, and . Nienhuis, Geometric properties of two-dimensional critical and tricritical Potts models, Physical Review E, vol.69, issue.2, p.26123, 2004.
DOI : 10.1103/PhysRevE.69.026123

J. Dubail, J. L. Jacobsen, and H. Saleur, Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model. arXiv:1010, 2010.

J. Dubail, J. L. Jacobsen, and H. Saleur, Critical exponents of domain walls in the two-dimensional Potts model, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.48, p.482002, 2010.
DOI : 10.1088/1751-8113/43/48/482002

R. Vasseur and J. L. Jacobsen, Critical properties of joint spin and Fortuin???Kasteleyn observables in the two-dimensional Potts model, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.16, p.165001, 2012.
DOI : 10.1088/1751-8113/45/16/165001

G. Delfino, M. Picco, R. Santachiara, and J. Viti, Spin clusters and conformal field theory, Journal of Statistical Mechanics: Theory and Experiment, vol.2013, issue.11, pp.2013-11011, 2013.
DOI : 10.1088/1742-5468/2013/11/P11011

URL : https://hal.archives-ouvertes.fr/hal-00905455

A. István, . Kovács, M. Eren-metin-elçi, F. Weigel, and . Iglói, Corner contribution to cluster numbers in the Potts model, 2013.

D. Stauffer and A. Aharony, Introduction to percolation theory, 1994.

J. L. Cardy, Critical percolation in finite geometries, Journal of Physics A: Mathematical and General, vol.25, issue.4, pp.201-206, 1992.
DOI : 10.1088/0305-4470/25/4/009

R. P. Langlands, C. Pichet, . Ph, Y. Pouliot, and . Saint-aubin, On the universality of crossing probabilities in two-dimensional percolation, Journal of Statistical Physics, vol.56, issue.3-4, pp.553-574, 1992.
DOI : 10.1007/BF01049720

T. Haru and . Pinson, Critical percolation on the torus, J. Stat. Phys, vol.75, issue.5-6, pp.1167-1177, 1994.

G. M. Watts, A crossing probability for critical percolation in two dimensions, Journal of Physics A: Mathematical and General, vol.29, issue.14, p.363, 1996.
DOI : 10.1088/0305-4470/29/14/002

J. Cardy, Crossing formulae for critical percolation in an annulus, Journal of Physics A: Mathematical and General, vol.35, issue.41, pp.565-572, 2002.
DOI : 10.1088/0305-4470/35/41/102

E. Lapalme and Y. Saint-aubin, Crossing probabilities on same-spin clusters in the two-dimensional Ising model, Journal of Physics A: Mathematical and General, vol.34, issue.9, pp.1825-1835, 2001.
DOI : 10.1088/0305-4470/34/9/302

L. Arguin and Y. Saint-aubin, Non-unitary observables in the 2d critical Ising model, Physics Letters B, vol.541, issue.3-4, pp.384-389, 2002.
DOI : 10.1016/S0370-2693(02)02228-1

M. Bauer, D. Bernard, and K. Kytölä, Multiple Schramm???Loewner Evolutions and Statistical Mechanics Martingales, Journal of Statistical Physics, vol.557, issue.3, pp.5-61125, 2005.
DOI : 10.1007/s10955-005-7002-5

URL : https://hal.archives-ouvertes.fr/hal-00023298

J. Michael and . Kozdron, Using the Schramm?Loewner evolution to explain certain non-local observables in the 2D critical Ising model, J. Phys. A: Math. Theo, vol.42, issue.26, p.265003, 2009.

J. Dubail, J. L. Jacobsen, and H. Saleur, Conformal boundary conditions in the critical model and dilute loop models, Nuclear Physics B, vol.827, issue.3, pp.457-502, 2010.
DOI : 10.1016/j.nuclphysb.2009.10.016

URL : https://hal.archives-ouvertes.fr/hal-00382588

O. Schramm, Scaling limits of loop-erased random walks and uniform spanning trees, Israel Journal of Mathematics, vol.111, issue.1, pp.221-288, 2000.
DOI : 10.1007/BF02803524

G. F. Lawler, O. Schramm, and W. Werner, On the scaling limit of planar self-avoiding walk, Proc. Sympos. Pure Math, pp.339-364, 2004.
DOI : 10.1090/pspum/072.2/2112127

S. Smirnov, Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.3, p.239, 2001.
DOI : 10.1016/S0764-4442(01)01991-7

R. Langlands, P. Pouliot, and Y. Saint-aubin, Conformal invariance in two-dimensional percolation. Bulletin of the, pp.1-61, 1994.

B. Nienhuis, Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas, Journal of Statistical Physics, vol.49, issue.FS3, pp.5-6731, 1984.
DOI : 10.1007/BF01009437

B. Nienhuis, Coulomb gas formulation of two dimensional phase transitions, Phase Transitions and Critical Phenomena, vol.11, p.1, 1987.

P. Di-francesco, H. Saleur, and J. B. Zuber, Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models, Journal of Statistical Physics, vol.15, issue.1-2, pp.57-79, 1987.
DOI : 10.1007/BF01009954

L. Arguin, Homology of Fortuin-Kasteleyn clusters of Potts models on the torus, Journal of Statistical Physics, vol.109, issue.1/2, pp.301-310, 2002.
DOI : 10.1023/A:1019979326380

A. Morin-duchesne and Y. Saint-aubin, Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus, Physical Review E, vol.80, issue.2, p.21130, 2009.
DOI : 10.1103/PhysRevE.80.021130

K. Barros, P. L. Krapivsky, and S. Redner, Freezing into stripe states in two-dimensional ferromagnets and crossing probabilities in critical percolation, Physical Review E, vol.80, issue.4, p.40101, 2009.
DOI : 10.1103/PhysRevE.80.040101

J. Olejarz, P. L. Krapivsky, and S. Redner, Fate of 2D Kinetic Ferromagnets and Critical Percolation Crossing Probabilities, Physical Review Letters, vol.109, issue.19, p.195702, 2012.
DOI : 10.1103/PhysRevLett.109.195702

T. Blanchard and M. Picco, Frozen into stripes: Fate of the critical Ising model after a quench, Physical Review E, vol.88, issue.3, p.32131, 2013.
DOI : 10.1103/PhysRevE.88.032131

URL : https://hal.archives-ouvertes.fr/hal-00818107

T. Blanchard, L. F. Cugliandolo, and M. Picco, A morphological study of cluster dynamics between critical points, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.05, pp.2012-05026, 2012.
DOI : 10.1088/1742-5468/2012/05/P05026

URL : https://hal.archives-ouvertes.fr/hal-00683575

T. Blanchard, F. Corberi, L. F. Cugliandolo, and M. Picco, How soon after a zero-temperature quench is the fate of the Ising model sealed?, EPL (Europhysics Letters), vol.106, issue.6, p.66001, 2014.
DOI : 10.1209/0295-5075/106/66001

URL : https://hal.archives-ouvertes.fr/hal-00933708

R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 2008.
DOI : 10.1142/9789814415255_0002

P. , D. Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory, 1997.

J. Cardy, The number of incipient spanning clusters in two-dimensional percolation, Journal of Physics A: Mathematical and General, vol.31, issue.5, pp.105-110, 1998.
DOI : 10.1088/0305-4470/31/5/003

U. Wolff, Collective Monte Carlo Updating for Spin Systems, Physical Review Letters, vol.62, issue.4, p.361, 1989.
DOI : 10.1103/PhysRevLett.62.361

M. Robert, . Ziff, D. Christian, P. Lorenz, and . Kleban, Shape-dependent universality in percolation. Physica A: Statistical Mechanics and its Applications, pp.1-417, 1999.

G. Pruessner and N. R. Moloney, Winding Clusters in Percolation on the Torus and the M??bius Strip, Journal of Statistical Physics, vol.115, issue.3/4, pp.839-853, 2004.
DOI : 10.1023/B:JOSS.0000022376.25660.7b

A. Campa, T. Dauxois, and S. Ruffo, Statistical mechanics and dynamics of solvable models with long-range interactions, Physics Reports, vol.480, issue.3-6, pp.3-657, 2009.
DOI : 10.1016/j.physrep.2009.07.001

URL : https://hal.archives-ouvertes.fr/hal-00530806

A. Gabrielli, M. Joyce, and B. Marcos, Quasistationary States and the Range of Pair Interactions, Physical Review Letters, vol.105, issue.21, p.210602, 2010.
DOI : 10.1103/PhysRevLett.105.210602

URL : https://hal.archives-ouvertes.fr/hal-00908555

P. Fernanda, C. Da, T. N. Benetti, R. Teles, Y. Pakter et al., Ergodicity breaking and parametric resonances in systems with long-range interactions, Phys. Rev. Lett, vol.108, issue.14, p.140601, 2012.

M. Kastner, Diverging Equilibration Times in Long-Range Quantum Spin Models, Physical Review Letters, vol.106, issue.13, p.130601, 2011.
DOI : 10.1103/PhysRevLett.106.130601

T. Barthel, S. Dusuel, and J. Vidal, Entanglement Entropy beyond the Free Case, Physical Review Letters, vol.97, issue.22, p.220402, 2006.
DOI : 10.1103/PhysRevLett.97.220402

URL : http://arxiv.org/abs/cond-mat/0606436

T. Koffel, M. Lewenstein, and L. Tagliacozzo, Entanglement Entropy for the Long-Range Ising Chain in a Transverse Field, Physical Review Letters, vol.109, issue.26, p.267203, 2012.
DOI : 10.1103/PhysRevLett.109.267203

A. Cadarso, M. Sanz, M. M. Wolf, J. I. Cirac, and D. Pérez-garcía, Entanglement, fractional magnetization, and long-range interactions, Physical Review B, vol.87, issue.3, p.35114, 2013.
DOI : 10.1103/PhysRevB.87.035114

URL : http://arxiv.org/abs/1209.3898

J. W. Britton, B. C. Sawyer, A. C. Keith, C. Wang, J. K. Freericks et al., Engineered twodimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins, Nature, issue.7395, pp.484489-492, 2012.

R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 2008.
DOI : 10.1142/9789814415255_0002

G. Kenneth, M. E. Wilson, and . Fisher, Critical exponents in 3.99 dimensions, Phys. Rev. Lett, vol.28, issue.4, pp.240-243, 1972.

R. Guida and J. Zinn-justin, Critical exponents of the n-vector model, J. Phys. A: Math. Gen, issue.40, p.318103, 1998.

S. El-showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-duffin et al., Solving the 3D Ising model with the conformal bootstrap, Physical Review D, vol.86, issue.2, p.25022, 2012.
DOI : 10.1103/PhysRevD.86.025022

URL : https://hal.archives-ouvertes.fr/cea-00825766

J. Freeman and . Dyson, Existence of a phase-transition in a one-dimensional Ising ferromagnet, Commun. in Math. Phys, vol.12, issue.2, pp.91-107, 1969.

G. Gallavotti and S. Miracle-sole, Statistical mechanics of lattice systems, Communications in Mathematical Physics, vol.6, issue.5, pp.317-323, 1967.
DOI : 10.1007/BF01646445

E. Michael, S. Fisher, B. G. Ma, and . Nickel, Critical exponents for longrange interactions, Phys. Rev. Lett, vol.29, issue.14, pp.917-920, 1972.

M. Aizenman and R. Fernández, Critical exponents for long-range interactions, Letters in Mathematical Physics, vol.107, issue.1, pp.39-49, 1988.
DOI : 10.1007/BF00398169

J. Sak, Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions, Physical Review B, vol.8, issue.1, pp.281-285, 1973.
DOI : 10.1103/PhysRevB.8.281

Y. Yamazaki, Critical exponent ?? of isotropic spin systems with long and short-range interactions, Physics Letters A, vol.61, issue.4, pp.207-210, 1977.
DOI : 10.1016/0375-9601(77)90139-6

Y. Yamazaki, Comments on the critical behavior of isotropic spin systems with longand short-range interactions. Physica A: Statistical Mechanics and its Applications, pp.3-4446, 1978.

Y. Yamazaki, Critical behaviour of isotropic spin systems with long- and short-range interactions, Il Nuovo Cimento A, vol.49, issue.1, pp.59-77, 1980.
DOI : 10.1007/BF02911857

E. Luijten, W. J. Henk, and . Blöte, Boundary between Long-Range and Short-Range Critical Behavior in Systems with Algebraic Interactions, Physical Review Letters, vol.89, issue.2, p.25703, 2002.
DOI : 10.1103/PhysRevLett.89.025703

U. Wolff, Collective Monte Carlo Updating for Spin Systems, Physical Review Letters, vol.62, issue.4, p.361, 1989.
DOI : 10.1103/PhysRevLett.62.361

M. Picco, Critical behavior of the Ising model with long range interactions, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00714495

L. John and . Cardy, Scaling and Renormalization in Statistical Physics, 1996.

C. Itzykson and J. Drouffe, Statistical Field Theory: From Brownian Motion to Renormalization and Lattice Gauge Theory, 1991.

H. Kleinert and V. Schulte-frohlinde, Critical Properties of 4 -theories, World Scientific, 2001.

J. C. Le-guillou and J. Zinn-justin, -Vector Model in Three Dimensions from Field Theory, Physical Review Letters, vol.39, issue.2, pp.95-98, 1977.
DOI : 10.1103/PhysRevLett.39.95

URL : https://hal.archives-ouvertes.fr/hal-00261097

Y. Holovatch, Critical exponents of Ising-like systems in general dimensions, Theor Math Phys, pp.1099-1109, 1993.
DOI : 10.1007/BF01019073

T. Blanchard, M. Picco, and M. A. Rajabpour, Influence of long-range interactions on the critical behavior of the Ising model, EPL (Europhysics Letters), vol.101, issue.5, p.56003, 2013.
DOI : 10.1209/0295-5075/101/56003

URL : https://hal.archives-ouvertes.fr/hal-00771010

G. Tarjus, M. Baczyk, and M. Tissier, Avalanches and Dimensional Reduction Breakdown in the Critical Behavior of Disordered Systems, Physical Review Letters, vol.110, issue.13, p.135703, 2013.
DOI : 10.1103/PhysRevLett.110.135703

M. Baczyk, M. Tissier, G. Tarjus, and Y. Sakamoto, Dimensional reduction and its breakdown in the three-dimensional long-range random-field Ising model, Physical Review B, vol.88, issue.1, p.14204, 2013.
DOI : 10.1103/PhysRevB.88.014204

M. Baczyk, G. Tarjus, M. Tissier, and I. Balog, Fixed points and their stability in the functional renormalization group of random field models. arXiv:1312, 2013.

M. Baczyk, Influence du champ aléatoire et des interactions à longue portée sur le comportement critique du modèle d'Ising; une approche par le groupe de renormalisation non perturbatif, 2014.

M. Chiara and A. , Renormalization group and critical properties of Long Range models, 2013.

M. Chiara-angelini, G. Parisi, and F. Ricci-tersenghi, Relations between short-range and long-range Ising models, Physical Review E, vol.89, issue.6, p.62120, 2014.
DOI : 10.1103/PhysRevE.89.062120

E. Brezin, G. Parisi, and F. Ricci-tersenghi, The crossover region between long-range and short-range interactions for the critical exponents. arXiv:1407, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01023623