Non-Self Averaging in Autocorrelations for Potts Models on Quenched Random Gravity Graphs

TL;DR

This paper studies how certain statistical physics models behave on random graphs with fixed disorder, revealing non-self-averaging properties using a new scaling method applicable beyond the specific case.

Contribution

It introduces a novel scaling technique to detect non-self-averaging in autocorrelation times, demonstrated on Potts models on quenched random graphs.

Findings

Non-self-averaging observed in autocorrelation times for energy and magnetisation.

The scaling method is broadly applicable to other disordered systems.

Results highlight the impact of quenched connectivity disorder on model dynamics.

Abstract

We investigate the non-self-averaging properties of the dynamics of Ising, 4-state Potts and 10-state Potts models in single-cluster Monte Carlo simulations on quenched ensembles of planar, trivalent Phi3 random graphs, which we use as an example of relevant quenched connectivity disorder. We employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetisation in order to discern non-self-averaging. Although the specific results discussed here are for quenched random graphs, the method has quite general applicability.