Correlated correlation functions in random-bond ferromagnets

TL;DR

This paper investigates how weak disorder affects correlation functions in the 2D random-bond Potts model near Q=2 using perturbative renormalization group analysis, revealing observable cross-correlations and providing a method for scaling dimensions.

Contribution

It introduces a novel analysis of disorder-induced cross-correlations in correlation functions and a simple method for deriving local energy operator scaling dimensions.

Findings

Disorder induces cross-correlations between moments of correlation functions.

Observable effects in specific linear combinations of quenched correlation functions.

A new method for calculating scaling dimensions of local energy moments.

Abstract

The two-dimensional random-bond Q-state Potts model is studied for Q near 2 via the perturbative renormalisation group to one loop. It is shown that weak disorder induces cross-correlations between the quenched-averages of moments of the two-point spin/spin and energy/energy correlation functions, which should be observable numerically in specific linear combinations of various quenched correlation functions. The random-bond Ising model in (2+epsilon) dimensions is similarly treated. As a byproduct, a simple method for deriving the scaling dimensions of all moments of the local energy operator is presented.