Europhys. Lett.
Volume 48, Number 6, December 1999
Page(s) 655 - 661
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00534-y

Europhys. Lett, 48 (6), pp. 655-661 (1999)

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

M.-A. Lewis

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 in final form 20 October 1999)

PACS. 64.60Ak - Renormalization-group, fractal, and percolation studies of phase transitions.


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 q=3 model. RSB effects, which should increase in strength with moment, are unobserved.


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