Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts

TL;DR

This study uses a domain wall renormalization group approach in charge representation to analyze the XY model with quenched disorder, revealing new insights into phase existence and critical exponents in 2D and 3D.

Contribution

It introduces a charge-based RG method for the XY model with disorder, providing more accurate critical exponents and clarifying phase boundaries in 2D and 3D.

Findings

No ordered phase in 2D gauge glass

Ordered phase exists in 3D at low temperature

Supports finite-temperature spin glass order in 3D

Abstract

The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\pm J$ XY spin glass in 3D, we obtain a spin stiffness exponent $\theta_{s} \approx +0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain $\theta_{s}< 0$. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale $L$. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.