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Quelques aspects de physique statistique des systèmes corrélés

Abstract : 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.
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Contributor : Maxime Clusel <>
Submitted on : Wednesday, November 16, 2005 - 11:45:59 PM
Last modification on : Thursday, November 21, 2019 - 2:24:03 AM
Long-term archiving on: : Monday, September 20, 2010 - 1:14:50 PM


  • HAL Id : tel-00010753, version 2


Maxime Clusel. Quelques aspects de physique statistique des systèmes corrélés. Analyse de données, Statistiques et Probabilités []. Ecole normale supérieure de lyon - ENS LYON, 2005. Français. ⟨tel-00010753v2⟩



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