Spin--spin critical point correlation functions for the 2D random bond Ising and Potts models

TL;DR

This paper calculates higher-order corrections to spin-spin correlation functions at the critical point for 2D random bond Ising and Potts models, revealing how randomness affects critical behavior.

Contribution

It introduces a renormalisation group method to compute loop corrections to correlation functions in disordered 2D models, highlighting differences in critical exponent shifts.

Findings

Corrections produce crossover in amplitude for Ising model

Randomness shifts the critical exponent in Potts model

Comparison with numerical data discussed

Abstract

We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.