Large-q asymptotics of the random bond Potts model

TL;DR

This paper investigates the behavior of the random bond Potts model as the number of states q becomes very large, revealing asymptotic properties of the critical line, central charge, and magnetic exponent through numerical methods.

Contribution

It introduces a combined approach using the loop representation and Zamolodchikov's c-theorem to analyze the large-q asymptotics of the model.

Findings

Central charge c(q) behaves like 1/2 log_2(q) + O(1)

Bulk magnetic exponent x_1 tends to approximately 0.192 as q approaches infinity

Accurate numerical values for critical exponents at large q are obtained

Abstract

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.