Comportement critique de modèles bidimensionnels en présence de perturbations inhomogènes

Abstract : In this work we study the influence of different inhomogeneous perturbations on the critical behaviour of two-dimensional models. In the first part we consider the two-dimensional Ising model in a random surface field which is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by Monte Carlo simulations for various strengths of disorder. The calculated effective (temperature or size-dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the expected logarithmic corrections to the pure system's critical behaviour. In the second part we study the Ising model on the square lattice with biaxially correlated random couplings which is a relevant perturbation according to the extended Harris criterion. The problem is studied by large scale Monte Carlo simulations. The correlation length critical exponent n has the value expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density is larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined. Finally we consider the critical behaviour at an interface between two subsystems belonging to different universality classes, but having a common transition temperature. We solve this problem analytically in the frame of mean-field theory and present some phenomenological scaling arguments. A large variety of interface critical behaviour is obtained which is checked numerically on the example of two-dimensional q-state Potts models with 2
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Farkas Adam Bagaméry. Comportement critique de modèles bidimensionnels en présence de perturbations inhomogènes. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10024⟩. ⟨tel-01754321⟩

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