Numerical Study of Order in a Gauge Glass Model

TL;DR

This study uses a numerical defect energy scaling method to analyze the order in a 2D and 3D gauge glass model, providing new estimates of the stiffness exponent that suggest the lower critical dimension is below three.

Contribution

It introduces an exact numerical technique to evaluate defect energies and provides more accurate estimates of the stiffness exponent in gauge glass models.

Findings

Stiffness exponent in 2D is approximately -0.36.

Stiffness exponent in 3D is approximately +0.31.

Lower critical dimension is suggested to be less than three.

Abstract

The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state configuration for a given realization of disorder. A numerical technique, which is exact in principle, is used to evaluate this energy and to estimate the stiffness exponent $\theta$. This method gives $\theta = -0.36\pm0.013$ in 2d and $\theta = +0.31\pm 0.015$ in 3d, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than three. Some arguments in favor of these new estimates are given.