Scale Invariance and Self-averaging in disordered systems

TL;DR

This paper investigates the phenomenon of scale invariance and self-averaging in disordered ferromagnetic systems, revealing varying degrees of self-averaging violation near critical points in different models.

Contribution

It extends previous work on the random field Ising model to disordered Potts and Ising models in two dimensions, analyzing their self-averaging properties near criticality.

Findings

Random Potts model shows weaker violation of self-averaging than the random field case.

Random Ising model exhibits even weaker violations, possibly restoring self-averaging in the infinite volume limit.

Abstract

In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.