Critical points and quenched disorder: From Harris criterion to rare regions and smearing

TL;DR

This paper explores how quenched disorder affects phase transitions, showing that rare strong fluctuations can smear the transition and lead to static order in disordered systems, supported by theoretical and numerical analysis.

Contribution

It introduces a comprehensive analysis of disorder-induced smearing of phase transitions, extending Griffiths phenomena and providing numerical evidence for two-dimensional models.

Findings

Rare strong disorder fluctuations can destroy sharp phase transitions.

Smeared transitions allow static order to develop in disordered phases.

Numerical results support the theoretical predictions for 2D systems.

Abstract

We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system.