The three-dimensional gauge-glass model

TL;DR

This study explores the phase diagram of a 3D gauge glass model using Monte Carlo simulations, revealing distinct paramagnetic, ferromagnetic, and glassy phases with specific critical behaviors and a multicritical point.

Contribution

It provides the first detailed numerical analysis of the phase transitions and critical behaviors in a 3D gauge glass model with a specific disorder distribution.

Findings

Disorder is irrelevant at the paramagnetic-ferromagnetic transition, following 3D XY universality.

The paramagnetic-glassy transition exhibits gauge-glass universality with a large critical exponent.

A multicritical point exists at T=S=0.7840(2), connecting different phases.

Abstract

We investigate the temperature-disorder (T-S) phase diagram of a three-dimensional gauge glass model, which is a cubic-lattice nearest-neighbor XY model with quenched random phase shifts A_xy at the bonds, by numerical Monte Carlo simulations. We consider the uncorrelated phase-shift distribution P(A_xy)\sim \exp[(cos A_xy)/S], which has the pure XY model and the uniform distribution of random shifts as extreme cases at S=0 and S->infty respectively, and which gives rise to equal magnetic and overlap correlation functions when T=S. While the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small S) and a glassy phase at large disorder (large S). These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random shifts turns out to be irrelevant at the paramagnetic-ferromagnetic transition line, where the critical behavior belongs to the 3D XY universality class of pure systems; disorder gives only rise to very slowly decaying scaling corrections. The glassy critical behavior along the finite-temperature paramagnetic-glassy transition line belongs to the gauge-glass universality class, with a quite large critical exponent nu=3.2(4). These transition lines meet at a multicritical point M, located at T=S=0.7840(2). The low-temperature ferromagnetic and glassy phases are separated by a third transition line, from M down to the T=0 axis, which is slightly reentrant.