Monte Carlo Study of the Critical Behavior of Random Bond Potts Models

TL;DR

This paper uses Monte Carlo simulations to study the critical behavior of two-dimensional random bond Potts models, revealing multifractal correlation functions and a single correlation length exponent near the pure Ising value.

Contribution

Introduces a simple scheme for generating continuous self-dual interaction distributions and analyzes multifractal behavior in the critical regime.

Findings

Multifractal behavior observed at the critical point.

Estimated exponents for various moments of correlation functions.

Single correlation length exponent close to the Ising value for q=8.

Abstract

We present results of Monte Carlo simulations of random bond Potts models in two dimensions, for different numbers of Potts states, q. We introduce a simple scheme which yields continuous self-dual distributions of the interactions. As expected, we find multifractal behavior of the correlation functions at the critical point and obtain estimates of the exponent eta_n for several moments, n, of the correlation functions, including typical (n -> 0), average (n=1) and others. In addition, for q=8, we find that there is only a single correlation length exponent describing the correlation length away from criticality. This is numerically very close to the pure Ising value of unity.