A. M. Salzberg and S. Prager, Equation of State for a Two???Dimensional Electrolyte, The Journal of Chemical Physics, vol.38, issue.10
DOI : 10.1063/1.1733553

V. L. Berezinskii, Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems, Sov. Phys. JETP, vol.32, p.493, 1971.

J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, Journal of Physics C: Solid State Physics, vol.6, issue.7, p.1181, 1973.
DOI : 10.1088/0022-3719/6/7/010

J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model, Physical Review B, vol.16, issue.3, p.1217, 1977.
DOI : 10.1103/PhysRevB.16.1217

M. R. Beasley, J. E. Mooij, and T. P. Orlando, Possibility of Vortex-Antivortex Pair Dissociation in Two-Dimensional Superconductors, Physical Review Letters, vol.42, issue.17, p.1165, 1979.
DOI : 10.1103/PhysRevLett.42.1165

S. A. Wolf, D. U. Gubser, W. W. Fuller, J. C. Garland, and R. S. Newrock, Two-Dimensional Phase Transition in Granular NbN Films, Physical Review Letters, vol.47, issue.15, p.1071, 1981.
DOI : 10.1103/PhysRevLett.47.1071

D. J. Resnick, J. C. Garland, J. T. Boyd, S. Shoemaker, and R. S. Newrock, Kosterlitz-Thouless Transition in Proximity-Coupled Superconducting Arrays, Physical Review Letters, vol.47, issue.21, p.1542, 1981.
DOI : 10.1103/PhysRevLett.47.1542

P. Minnhagen, Universal resistive transition for two-dimensional superconductors, Physical Review B, vol.24, issue.11, p.6758, 1981.
DOI : 10.1103/PhysRevB.24.6758

D. R. Nelson and J. M. Kosterlitz, Universal Jump in the Superfluid Density of Two-Dimensional Superfluids, Physical Review Letters, vol.39, issue.19, p.1201, 1977.
DOI : 10.1103/PhysRevLett.39.1201

V. Ambegaokar, B. I. Halperin, D. R. Nelson, and E. D. Siggia, Dissipation in Two-Dimensional Superfluids, Physical Review Letters, vol.40, issue.12, p.783, 1978.
DOI : 10.1103/PhysRevLett.40.783

D. J. Bishop and J. D. Reppy, Films, Physical Review Letters, vol.40, issue.26, p.1727, 1978.
DOI : 10.1103/PhysRevLett.40.1727

D. J. Bishop and J. D. Reppy, films, Physical Review B, vol.22, issue.11, p.5171, 1980.
DOI : 10.1103/PhysRevB.22.5171

R. J. Birgeneau and J. D. Litster, Bond orientational order model for smectic B liquid crystals, Journal de Physique Lettres, vol.39, issue.21, p.399, 1978.
DOI : 10.1051/jphyslet:019780039021039900
URL : https://hal.archives-ouvertes.fr/jpa-00231527

S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Continuous quantum phase transitions, Reviews of Modern Physics, vol.69, issue.1, p.315, 1997.
DOI : 10.1103/RevModPhys.69.315
URL : http://arxiv.org/abs/cond-mat/9609279

A. Trombettoni, A. Smerzi, and P. Sodano, Observable signature of the Berezinskii???Kosterlitz???Thouless transition in a planar lattice of Bose???Einstein condensates, New Journal of Physics, vol.7, p.57, 2005.
DOI : 10.1088/1367-2630/7/1/057

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, Berezinskii???Kosterlitz???Thouless crossover in a trapped atomic gas, Nature, vol.39, issue.7097, p.1118, 2006.
DOI : 10.1038/nature04851
URL : https://hal.archives-ouvertes.fr/hal-00067716

V. M. Vinokur, T. I. Baturina, M. V. Fistul, A. Yu, M. R. Mironov et al., Superinsulator and quantum synchronization, Nature, vol.16, issue.7187, p.613, 2008.
DOI : 10.1038/nature06837

T. I. Baturina and V. M. Vinokur, Superinsulator???superconductor duality in two dimensions, Annals of Physics, vol.331, p.236, 2013.
DOI : 10.1016/j.aop.2012.12.007

S. T. Bramwell and P. C. Holdsworth, Magnetization and universal sub-critical behaviour in two-dimensional XY magnets, Journal of Physics: Condensed Matter, vol.5, issue.4, p.53, 1993.
DOI : 10.1088/0953-8984/5/4/004

S. Bramwell and P. C. Holdsworth, Magnetization: A characteristic of the Kosterlitz-Thouless-Berezinskii transition, Physical Review B, vol.49, issue.13, p.8811, 1994.
DOI : 10.1103/PhysRevB.49.8811

A. Taroni, S. T. Bramwell, and P. C. Holdsworth, Universal window for two-dimensional critical exponents, Journal of Physics: Condensed Matter, vol.20, issue.27, p.275233, 2008.
DOI : 10.1088/0953-8984/20/27/275233

A. Vallat and H. Beck, model on a torus, Physical Review B, vol.50, issue.6, p.4015, 1994.
DOI : 10.1103/PhysRevB.50.4015

J. Villain, Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet, Journal de Physique, vol.36, issue.6, p.581, 1975.
DOI : 10.1051/jphys:01975003606058100
URL : https://hal.archives-ouvertes.fr/jpa-00208289

A. C. Maggs and V. Rossetto, Local Simulation Algorithms for Coulomb Interactions, Physical Review Letters, vol.88, issue.19, 2002.
DOI : 10.1103/PhysRevLett.88.196402

N. D. Mermin and H. Wagner, Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models, Physical Review Letters, vol.17, issue.22, p.1133, 1966.
DOI : 10.1103/PhysRevLett.17.1133

D. J. Thouless, Topology of Strongly Correlated Systems: Edited by P Bicudo et al, World Scientific, 2001.

R. G. Palmer, Broken ergodicity, Advances in Physics, vol.25, issue.6, p.669, 1982.
DOI : 10.1080/00018738200101438

C. Coulomb, Second mémoire sur l'´ electricité et le magnétisme, Histoire de l'Académie Royale des Sciences, pp.578-1785

W. Janke and K. Nather, model, Physical Review B, vol.48, issue.21, p.15807, 1993.
DOI : 10.1103/PhysRevB.48.15807
URL : https://hal.archives-ouvertes.fr/hal-00003802

L. Levrel, F. Alet, J. Rottler, and A. C. Maggs, Local simulation algorithms for Coulombic interactions, Pramana, vol.67, issue.6, p.1001, 2005.
DOI : 10.1007/BF02704162

V. Rossetto, Mécanique statistique de systèmes sous constraintes : topologie de l'ADN et simulationsélectrostatiqueslationsélectrostatiques .Deuxì eme partie : Simulations locales d'interactions coulombiennes, 2002.

A. C. Maggs, Auxiliary field Monte Carlo for charged particles, The Journal of Chemical Physics, vol.120, issue.7, p.3108, 2004.
DOI : 10.1063/1.1642587

A. C. Maggs and J. Rottler, Auxiliary field simulation and Coulomb's law, Computer Physics Communications, vol.169, issue.1-3, p.160, 2005.
DOI : 10.1016/j.cpc.2005.03.037

L. Levrel and A. C. Maggs, Boundary conditions in local electrostatics algorithms, The Journal of Chemical Physics, vol.128, issue.21, p.214103, 2008.
DOI : 10.1063/1.2918365

S. Raghu, D. Podolsky, A. Vishwanath, and D. A. Huse, Vortex-dynamics approach to the Nernst effect in extreme type-II superconductors dominated by phase fluctuations, Physical Review B, vol.78, issue.18, p.184520, 2008.
DOI : 10.1103/PhysRevB.78.184520

S. T. Banks, Fluctuations of Global Quantities in Highly Correlated Systems, 2005.

P. Archambault, S. T. Bramwell, and P. C. Holdsworth, Magnetic fluctuations in a finite two-dimensional model, Journal of Physics A: Mathematical and General, vol.30, issue.24, p.8363, 1997.
DOI : 10.1088/0305-4470/30/24/005

P. Minnhagen and B. J. Kim, Direct evidence of the discontinuous character of the Kosterlitz-Thouless jump, Physical Review B, vol.67, issue.17, p.172509, 2003.
DOI : 10.1103/PhysRevB.67.172509

J. M. Kosterlitz, The critical properties of the two-dimensional xy model, Journal of Physics C: Solid State Physics, vol.7, issue.6, p.1046, 1974.
DOI : 10.1088/0022-3719/7/6/005

J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Erratum: Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model, Physical Review B, vol.17, issue.3, p.1477, 1978.
DOI : 10.1103/PhysRevB.17.1477

J. Tobochnik and G. V. Chester, Monte Carlo study of the planar spin model, Physical Review B, vol.20, issue.9, p.3761, 1979.
DOI : 10.1103/PhysRevB.20.3761

D. C. Mattis, Transfer matrix in plane-rotator model, Physics Letters A, vol.104, issue.6-7, p.357, 1984.
DOI : 10.1016/0375-9601(84)90816-8

H. Weber and P. Minnhagen, model, Physical Review B, vol.37, issue.10, p.5986, 1988.
DOI : 10.1103/PhysRevB.37.5986
URL : https://hal.archives-ouvertes.fr/in2p3-00004531

C. M. Lapilli, P. Pfeifer, and C. Wexler, Universality Away from Critical Points in Two-Dimensional Phase Transitions, Physical Review Letters, vol.96, issue.14, p.140603, 2006.
DOI : 10.1103/PhysRevLett.96.140603

S. G. Carling, P. Day, and D. Visser, O, n=2-4, Journal of Physics: Condensed Matter, vol.7, issue.9, p.109, 1995.
DOI : 10.1088/0953-8984/7/9/002

S. J. Clarke, A. Harrison, T. E. Mason, G. J. Mcintyre, and D. Visser, O, Magnetic ordering and fluctuations in the S= 1/2 square Heisenberg antiferromagnet Cu(DCO 2 ) 2 .4D 2 O, p.71, 1992.
DOI : 10.1088/0953-8984/4/4/003
URL : https://hal.archives-ouvertes.fr/in2p3-00071159

T. Chattopadhyay, P. J. Brown, A. A. Stepanov, A. I. Zvyagin, S. N. Barilo et al., Antiferromagnetic ordering in Gd 2 CuO 4, J. Magn. Magn. Mater, vol.104, p.607, 1992.

C. Bellitto, P. Filaci, and S. Patrizio, Zero-field magnetic susceptibility study of the magnetic phase transition in the two-dimensional ionic ferromagnet bis(benzylammonium) tetrabromochromate(II), (C6H5CH2NH3)2CrBr4, Inorganic Chemistry, vol.26, issue.1, p.191, 1987.
DOI : 10.1021/ic00248a037

A. Paduan-filho and C. C. Becerra, Magnetic properties and critical behavior of the pure and diluted two-dimensional weak ferromagnet (CH[sub 3]NH[sub 3])[sub 2]Mn[sub 1???x]Cd[sub x]Cl[sub 4], Journal of Applied Physics, vol.91, issue.10, p.8249, 2002.
DOI : 10.1063/1.1448789

K. W. Krämer, H. U. Güdel, P. Fischer, F. Fauth, M. T. Fernandez-diaz et al., Triangular antiferromagnetic order in the honeycomb layer lattice of, The European Physical Journal B, vol.18, issue.1, p.39, 2000.
DOI : 10.1007/s100510070075

F. C. Coomer, V. Bondah-jagalu, K. J. Grant, A. Harrison, G. J. Mcintyre et al., ), Physical Review B, vol.75, issue.9, p.94424, 2007.
DOI : 10.1103/PhysRevB.75.094424

M. Pärnaste, M. Marcellini, E. Holmström, N. Bock, J. Fransson et al., Dimensionality crossover in the induced magnetization of Pd layers, Journal of Physics: Condensed Matter, vol.19, issue.24, p.246213, 2007.
DOI : 10.1088/0953-8984/19/24/246213

M. Pärnaste, M. Marcellini, and B. Hjörvarsson, Oscillatory exchange coupling in the two-dimensional limit, Journal of Physics: Condensed Matter, vol.17, issue.44, p.477, 2005.
DOI : 10.1088/0953-8984/17/44/L03

F. Huang, M. T. Kief, G. J. Mankey, and R. F. Willis, Magnetism in the few-monolayers limit: A surface magneto-optic Kerr-effect study of the magnetic behavior of ultrathin films of Co, Ni, and Co-Ni alloys on Cu(100) and Cu(111), Ni, and Co-Ni alloys on Cu(100) and Cu, p.3962, 1994.
DOI : 10.1103/PhysRevB.49.3962

F. Huang, G. J. Mankey, M. T. Kief, and R. F. Willis, Finite???size scaling behavior of ferromagnetic thin films, Journal of Applied Physics, vol.73, issue.10, p.6760, 1993.
DOI : 10.1063/1.352477

M. Gajdzik, T. Trappmann, C. Sürgers, and H. V. Löhneysen, Morphology and magnetic properties of submonolayer Gd films, Physical Review B, vol.57, issue.6, p.3525, 1998.
DOI : 10.1103/PhysRevB.57.3525

W. C. Chew, Electromagnetic theory on a lattice, Journal of Applied Physics, vol.75, issue.10, p.4843, 1994.
DOI : 10.1063/1.355770

F. L. Spitzer, Graduate Texts in Mathematics, 1964.

J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. Newman, The Theory of Critical Phenomena: An Introduction to the Renormalization Group, 1992.

A. Liebig, P. T. Korelis, M. Ahlberg, and B. Hjörvarsson, magnets, Physical Review B, vol.84, issue.2, p.24430, 2011.
DOI : 10.1103/PhysRevB.84.024430

S. Gayen, M. K. Sanyal, A. Sarma, M. Wolff, K. Zhernenkov et al., Polarized neutron reflectivity study of spin vortices formed in Gd-based Langmuir-Blodgett films, Physical Review B, vol.82, issue.17, p.174429, 2010.
DOI : 10.1103/PhysRevB.82.174429

M. K. Mukhopadhyay, M. K. Sanyal, T. Sakakibara, V. Leiner, R. M. Dalgliesh et al., Polarized neutron scattering and sub-Kelvin magnetization measurements in two-dimensional gadolinium stearate Langmuir-Blodgett films, Physical Review B, vol.74, issue.1, p.14402, 2006.
DOI : 10.1103/PhysRevB.74.014402

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, vol.415, issue.6867, p.39, 2002.
DOI : 10.1038/415039a

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator, Physical Review Letters, vol.92, issue.13, p.130403, 2004.
DOI : 10.1103/PhysRevLett.92.130403

N. Murray, M. Krygier, M. Edwards, K. C. Wright, G. K. Campbell et al., Probing the circulation of ring-shaped Bose-Einstein condensates, Physical Review A, vol.88, issue.5, p.53615, 2013.
DOI : 10.1103/PhysRevA.88.053615