Renormalisation group calculation of correlation functions for the 2D random bond Ising and Potts models

TL;DR

This paper uses renormalisation group methods to analyze how randomness affects correlation functions in 2D Ising and Potts models, revealing amplitude crossovers and critical exponent shifts at criticality.

Contribution

It introduces a renormalisation approach for perturbation series around conformal field theories to study the effects of randomness on correlation functions in 2D models.

Findings

Amplitude crossover in Ising model without changing critical exponent

Shift in critical exponent for the Potts model due to randomness

Comparison with numerical data discussed briefly

Abstract

We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which doesn't change the critical exponent, and a shift in the critical exponent produced by randomness in the case of the Potts model. A comparison with numerical data is discussed briefly.