Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit

TL;DR

This paper investigates the excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit, combining conformal field theory techniques with numerical calculations to reveal universal properties and estimate the central charge.

Contribution

It provides a novel calculation of excess entropy and central charge for the large-Q limit of the 2D random-bond Potts model using conformal field theory and numerical methods.

Findings

Excess entropy is proportional to contour length with universal logarithmic corner corrections.

The central charge approaches approximately 0.74 as Q tends to infinity.

Results are consistent with previous finite-Q estimates of the central charge.

Abstract

We consider the random-bond Potts model in the large-$Q$ limit and calculate the excess entropy, $S_{\Gamma}$, of a contour, $\Gamma$, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by $\Gamma$. In two dimensions $S_{\Gamma}$ is proportional to the length of $\Gamma$, to which - at the critical point - there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: $\lim_{Q \to \infty}c(Q)/\ln Q =0.74(2)$, close to previous estimates calculated at finite values of $Q$.