Gauge glass in two dimensions

TL;DR

This paper investigates the two-dimensional gauge glass model, demonstrating that vortex screening leads to a power-law divergence of the glass correlation length with temperature, supporting the existence of a low-temperature glass phase.

Contribution

It provides a detailed analytical and numerical analysis showing vortex screening effects and power-law behaviors in the 2D gauge glass, clarifying the nature of its low-temperature phase.

Findings

Vortex screening eliminates logarithmic divergence of vortex energy.

Power-law decay of Coulomb interaction between vortices.

Finite diffusion constant for free vortices at all T > 0.

Abstract

The gauge glass model offers an interesting example of a randomly frustrated system with a continuous O(2) symmetry. In two dimensions, the existence of a glass phase at low temperatures has long been disputed among numerical studies. To resolve this controversy, we examine the behavior of vortices whose movement generates phase slips that destroy phase rigidity at large distances. Detailed analytical and numerical studies of the corresponding Coulomb gas problem in a random potential establish that the ground state, with a finite density of vortices, is polarizable with a scale-dependent dielectric susceptibility. Screening by vortex/antivortex pairs of arbitrarily large size is present to eliminate the logarithmic divergence of the Coulomb energy of a single vortex. The observed power-law decay of the Coulomb interaction between vortices with distance in the ground state leads to a power-law divergence of the glass correlation length with temperature $T$. It is argued that free vortices possess a bound excitation energy and a nonzero diffusion constant at any $T>0$.