Disorder-induced rounding of certain quantum phase transitions

TL;DR

This paper investigates how quenched disorder affects quantum phase transitions with over-damped dynamics, showing that disorder can round the transition and alter the relation between order parameter, coupling, and temperature.

Contribution

It demonstrates that quenched disorder causes rounding of certain quantum phase transitions and modifies the dependence of order parameters and critical temperatures, supported by Lifshitz-tail arguments and simulations.

Findings

Disorder destroys sharp phase transitions by rounding in systems with Ising symmetry.

Order parameter exhibits exponential dependence on coupling due to rare regions.

Finite temperature effects restore phase transitions, leading to double-exponential relations.

Abstract

We study the influence of quenched disorder on quantum phase transitions in systems with over-damped dynamics. For Ising order parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double-exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model system.