Typical versus average helicity modulus in the three-dimensional gauge glass: Understanding the vortex glass phase

TL;DR

This study uses Monte Carlo simulations to analyze the distribution of the helicity modulus in the 3D gauge glass, revealing that the typical (median) value remains nonzero in the vortex glass phase, challenging previous claims about superfluid density vanishing.

Contribution

It demonstrates that the median helicity modulus, modeled by a generalized extreme-value distribution, provides a reliable observable for identifying the vortex glass transition.

Findings

The distribution of the helicity modulus is well described by a generalized extreme-value distribution.

The finite-size scaling of the median yields a critical temperature and exponents consistent with prior studies.

The median helicity modulus remains nonzero in the vortex glass phase, suggesting a finite superfluid density.

Abstract

We numerically compute the helicity modulus of the three-dimensional gauge glass by Monte Carlo simulations. Because the average free energy is independent of a twist angle, it is expected that the average helicity modulus, directly related to the superfluid density, vanishes when simulations are performed with periodic boundary conditions. This is not necessarily the case for the typical (median) value, which is nonzero, because the distribution of the helicity modulus among different disorder realizations is very asymmetric. We show that the data for the helicity modulus distribution are well described by a generalized extreme-value distribution with a nonzero location parameter (most probable value). A finite-size scaling analysis of the location parameter yields a critical temperature and critical exponents in agreement with previous results. This suggests that the location parameter is a good observable. There have been conflicting claims as to whether the superfluid density vanishes in the vortex glass phase, with Fisher et al. [Phys. Rev. B 43, 130 (1991)] arguing that it is finite and Korshunov [Phys. Rev. B 63, 174514 (2001)] predicting that it is zero. Because the gauge glass is commonly used to describe the vortex glass in high-temperature superconductors, we discuss this issue in light of our results on the gauge glass.