Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models

TL;DR

This study uses transfer matrix methods to analyze the universality and multifractal properties of spin-spin correlation functions in disordered Potts models near the Ising point, comparing numerical results with perturbative theories.

Contribution

It provides a detailed numerical investigation of correlation functions in disordered Potts models, confirming the validity of replica symmetric perturbative results and exploring multifractal behavior.

Findings

Numerical data supports replica symmetric perturbative calculations.

Universality is confirmed across different disorder distributions.

Multifractal behavior of higher moments and typical correlations is observed.

Abstract

We report a transfer matrix study of the random bond $q-$state Potts model in the vicinity of the Ising model $q=2$. We draw attention to a precise determination of magnetic scaling dimensions in order to compare with perturbative results. Universality is checked by the computation of the spin-spin correlation function decay exponent obtained with different types of probability distributions of the coupling strengths. Our numerical data, compared to perturbative results for the second moment of the correlation function, obtained with both replica symmetry and replica symmetry breaking schemes, are conclusively in favour of the replica symmetric calculations. The multifractal behaviour of higher moments as well as that of typical correlation functions are also investigated and a comparison is made with the perturbative expansions. Finally, the shape of the correlation function probability distribution is analyzed.