Further evidence of the absence of replica symmetry breaking in random bond Potts models

Laboratoire de Physique Théorique et des Hautes Energies, Universités Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Boîte 126, Tour 16, 1er étage - 4 pl. Jussieu, 75251 Paris Cedex 05, France

Received: 12 July 1999
Accepted: 20 October 1999

Abstract

In this letter we present supporting evidence for the replica symmetric approach to the random bond q-state Potts models. The evidence is statistically strong enough to reject the applicability of the Parisi replica symmetry breaking scheme to this class of models. The test we use is a generalization of one formerly proposed by Dotsenko et al. (Nucl. Phys. B, 520 (1998) 633) and consists in measuring scaling laws of disordered-averaged moments of the spin-spin correlation functions. Numerical results, obtained via Monte Carlo simulations for several values of q, are shown to be in fair agreement with the replica symmetric values computed by using perturbative CFT (Dotsenko Vik. S. et al., Nucl. Phys. B, 520 (1998) 633; Lewis M.-A., Europhys. Lett., 43 (1998) 189) for the second and third moments of the model. RSB effects, which should increase in strength with moment, are unobserved.