THE RANDOM POTTS MODEL

Bertrand Berche (Personal webpage), Christophe Chatelain (Personal webpage)

Influence of uncorrelated, quenched disorder on the phase transition of two dimensional Potts models will be reviewed. After an introduction where the conditions of relevance of quenched randomness on phase transitions are exemplified by some experimental measurements, the results of perturbative and numerical investigations in the case of the Potts model will be presented. The Potts model is of particular interest, since it an have in the pure case a second-order or a first-order transition, depending on the number of states per spin. In 2D, transfer matrix calculations and Monte Carlo simulations are used in order to check the validity of conformal invariance methods in disordered systems. These techniques are then used to investigate the universality class of the disordered Potts model, in both regimes of the pure model phase transitions. A test of replica symmetry is made possible through a study of multiscaling properties.