Effects of Quenched Randomness on Classical and Quantum Phase Transitions

TL;DR

This paper investigates how quenched randomness influences phase transitions in classical and quantum lattice systems, demonstrating that disorder can suppress first-order transitions in low-dimensional cases.

Contribution

It provides rigorous proofs that certain low-dimensional quantum lattice systems cannot have first-order phase transitions when subjected to specific types of quenched disorder.

Findings

Disorder prevents first-order transitions in low-dimensional quantum systems.

Quantum lattice systems with continuous symmetry are affected similarly.

Theoretical framework applies to a broad class of models.

Abstract

This dissertation describes the effect of quenched randomness on first order phase transitions in lattice systems, classical and quantum. It is proven that a large class of quantum lattice systems in low dimension (d <= 2 or, with suitable continuous symmetry, d <= 4) cannot exhibit first-order phase transitions in the presence of suitable ("direct") quenched disorder.