Some aspects of statistical physics of correlated systems
Quelques aspects de physique statistique des systèmes corrélés
Résumé
This thesis deals with different aspects of statistical physics of correlated systems. The first part
is related to the fluctuations of global quantities in correlated systems. Various studies clam that such
fluctuations are well described by the BHP distribution. We use the 2D Ising model to test and quantify
this proposition. Using observations from Monte Carlo simulations, we build a theoretical analysis, showing
that the apparent universality of the BHP distribution is related to the Gaussian model obtained from
perturbation expansion. Deviations from BHP, due to a non-linear term are expected. In the second part
we consider a new model for a 1/f classical intermittent noise and study its effects on the dephasing of a
two-level system.Within this model, the evolution of the relative phase between the two states is described as
a continuous time random walk. Using renewal theory, we find exact expressions for the dephasing factor and
identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point
out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including
some new anomalous and aging dephasing scenarios. In the last part we present an alternative method to
obtain some exact results for the 2D Ising model with a boundary magnetic field, for a finite size system.
This method is a generalisation of ideas from Plechko presented for the 2D Ising model in zero field, based
on the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for a
general configuration of the boundary magnetic field. When the magnetic field is homogeneous, our results
are in agreement with McCoy and Wu's previous work. This 1D action is used to compute in an efficient
way the free energy in a special case of inhomogeneous boundary magnetic field. This allows us to compute
the phase diagram of a wetting transition induced by a boundary defect.
is related to the fluctuations of global quantities in correlated systems. Various studies clam that such
fluctuations are well described by the BHP distribution. We use the 2D Ising model to test and quantify
this proposition. Using observations from Monte Carlo simulations, we build a theoretical analysis, showing
that the apparent universality of the BHP distribution is related to the Gaussian model obtained from
perturbation expansion. Deviations from BHP, due to a non-linear term are expected. In the second part
we consider a new model for a 1/f classical intermittent noise and study its effects on the dephasing of a
two-level system.Within this model, the evolution of the relative phase between the two states is described as
a continuous time random walk. Using renewal theory, we find exact expressions for the dephasing factor and
identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point
out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including
some new anomalous and aging dephasing scenarios. In the last part we present an alternative method to
obtain some exact results for the 2D Ising model with a boundary magnetic field, for a finite size system.
This method is a generalisation of ideas from Plechko presented for the 2D Ising model in zero field, based
on the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for a
general configuration of the boundary magnetic field. When the magnetic field is homogeneous, our results
are in agreement with McCoy and Wu's previous work. This 1D action is used to compute in an efficient
way the free energy in a special case of inhomogeneous boundary magnetic field. This allows us to compute
the phase diagram of a wetting transition induced by a boundary defect.
Les travaux regroupés dans cette th`ese traitent de différents aspects de la physique statistique dessystèmes corrélés. Dans la première partie de cette thèse on s'intéresse aux fluctuations de grandeurs globalesdans les systèmes corrélés, dont de nombreux travaux sur des systèmes variés proposent qu'elles soientbien d´ecrites par la distribution BHP issue du modèle XY 2d. Le modèle d'Ising 2d est utilisé pour tester cette proposition et laquantifier. En utilisant des observations issues de simulations Monte Carlo, une étude analytique montre quel'apparente universalité de BHP est reliée au modèle gaussien obtenu par perturbation. et que des écarts àBHP d'importance variable existe, provenant de la contribution d'un terme non-gaussien. Dans la secondepartie, on s'intéresse à l'étude de la décohérence d'un système quantique à deux niveaux, induite par unbruit intermittent présentant un spectre en 1/f et du vieillissement. Un tel bruit peut schématiser l'effet d'unenvironnement corrélé sur un Qbit. En utilisant des résultats de probabilité, on peut calculer le facteur dedécohérence dans de nombreux régimes. On obtient alors des scénarios de décohérence anormaux, présentantune décroissance en loi de puissance aux temps longs, ainsi que de la non-stationnarité. Enfin la dernièrepartie est dédiée `a l'étude des solutions exactes du modèle d'Ising 2d classique, avec un champ magnétiquesur un bord. En généralisant une méthode due à Plechko, on obtient la fonction de partition de ce systèmeau moyen d'une action gaussienne fermionique unidimensionnelle. Dans le cas d'un champ homogène, onretrouve les résultats précédents de McCoy et Wu. On peut aller au-delà en considérant le cas où le champmagnétique change de direction une fois au bord. Cette méthode permet alors de décrire une transition detype mouillage, induite par ce défaut d'orientation. Il est en particulier possible d'obtenir analytiquement lediagramme de phase de ce système.
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