Large-q asymptotics of the random bond Potts model

Details Large-q asymptotics of the random bond Potts model Large-q asymptotics of the random bond Potts model

1999-10-06

arxiv.org/abs/cond-mat/9910071v1

Phys. Rev. E 61, R13-16 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, no figures

Scientific paper

10.1103/PhysRevE.61.R13

We numerically examine the large-q asymptotics of the q-state random bond Potts model. Special attention is paid to the parametrisation of the critical line, which is determined by combining the loop representation of the transfer matrix with Zamolodchikov's c-theorem. Asymptotically the central charge seems to behave like c(q) = 1/2 log_2(q) + O(1). Very accurate values of the bulk magnetic exponent x_1 are then extracted by performing Monte Carlo simulations directly at the critical point. As q -> infinity, these seem to tend to a non-trivial limit, x_1 -> 0.192 +- 0.002.

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