Rare region effects at classical, quantum, and non-equilibrium phase transitions

TL;DR

This paper reviews how rare regions influence phase transitions across classical, quantum, and non-equilibrium systems, highlighting effects like Griffiths singularities and transition smearing, and provides a unifying theoretical framework.

Contribution

It offers a comprehensive unifying framework for understanding rare region effects across various types of phase transitions based on effective dimensionality.

Findings

Rare regions cause Griffiths singularities near phase transitions.

Strong disorder effects can lead to smearing of phase transitions.

Explicit examples include disordered Ising, Heisenberg models, and quantum magnets.

Abstract

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.