Skip to Main content Skip to Navigation
Theses

Etude de l'influence du désordre sur les propriétés critiques du modèle de Potts

Abstract : We present a numerical study of the critical properties of the two-dimensional q-state Potts model perturbed by disorder coupled to the energy density. The pure system undergoes a first-order phase transition when q>4 and a continuous one otherwise. We show that under the influence of a correlated disorder in one direction, the first-order regime disappears in favour of a continuous transition whose universality class is independent of the number of states q. We extend the study to several aperiodic modulations of exchange couplings which allow the control of the divergence of the geometrical fluctuations. The perturbation softens the transition of the 8-state Potts model and, for some of the sequences considered, the transition becomes continuous. We also considered the case of a homogeneous disorder. We confirm the assumption of a continuous transition for any finite value of q and show that the critical behaviour is controlled by a random fixed point depending on the value of q. We observed the compatibility of our numerical estimations with the expressions of profiles and correlation functions predicted by conformal invariance. Taking advantage of this validity of conformal invariance, we give accurate estimations of the critical exponents of the average quantities and of its moments. The results are compatible within error bars with perturbative expansions around q=2. They also exclude the possibility of spontaneous replica-symmetry breaking. Finally, we present preliminary results concerning the three-dimensional bond-diluted 4-state Potts model. The pure system undergoes a strong first order transition. We present numerical evidences of the existence of a second-order regime at strong dilution, and thus of a tricritical point.
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00001376
Contributor : Christophe Chatelain <>
Submitted on : Monday, June 3, 2002 - 10:14:43 AM
Last modification on : Thursday, November 12, 2020 - 3:42:03 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:30:37 PM

Identifiers

  • HAL Id : tel-00001376, version 1

Collections

Citation

Christophe Chatelain. Etude de l'influence du désordre sur les propriétés critiques du modèle de Potts. Mécanique statistique [cond-mat.stat-mech]. Université Henri Poincaré - Nancy I, 2000. Français. ⟨tel-00001376⟩

Share

Metrics

Record views

603

Files downloads

284