Random Z(2) Higgs Lattice Gauge Theory in Three Dimensions and its Phase Structure

TL;DR

This paper investigates the phase structure of a three-dimensional random Z(2) lattice gauge theory with Higgs fields, revealing how randomness affects phase transitions and the Higgs phase region through novel mean field theory and Monte Carlo simulations.

Contribution

It introduces a new mean field approach without replica symmetry assumptions and applies it alongside Monte Carlo simulations to analyze the phase diagram of the model.

Findings

Higgs phase region shrinks with increasing randomness p

First-order phase transition disappears for p ≥ 0.01

Monte Carlo results align with mean field predictions

Abstract

We study the three-dimensional random Z(2) lattice gauge theory with Higgs field, which has the link Higgs coupling $c_1 SUS$ and the plaquette gauge coupling $c_2 UUUU$. The randomness is introduced by replacing $c_1 \to -c_1$ for each link with the probability $p_1$ and $c_2 \to -c_2$ for each plaquette with the probability $p_2$. We calculate the phase diagram by a new kind of mean field theory that does not assume the replica symmetry and also by Monte Carlo simulations. For the case $p_1=p_2(\equiv p)$, the Monte Carlo simulations exhibit that (i) the region of the Higgs phase in the Coulomb-Higgs transition diminishes as $p$ increases, and (ii) the first-order phase transition between the Higgs and the confinement phases disappear for $p \ge p_c \simeq 0.01$. We discuss the implications of the results to the quantum memory studied by Kitaev et al. and the Z(2) gauge neural network on a lattice.