Absence of the Effects of Vortices in the Gauge Glass

TL;DR

This paper demonstrates that vortices do not influence the thermodynamic behavior of the gauge glass and Villain model, as shown through correlation functions calculated via the spin wave approximation, which is exact on the Nishimori line.

Contribution

It proves that vortices are irrelevant to the thermodynamics of these models by analytically showing the exactness of the spin wave approximation on the Nishimori line.

Findings

Spin wave approximation yields exact solutions on the Nishimori line.

Vortices do not affect the thermodynamic properties in these models.

Results are applicable across all dimensions, including two-dimensional cases.

Abstract

We calculate several correlation functions and distribution functions of dynamical variables for the gauge glass and the Villain model using the spin wave approximation and the gauge transformation. The results show that the spin wave approximation gives the exact solutions on the Nishimori line in the phase diagram. This implies that vortices play no role in the thermodynamic behavior of the system as long as some correlation and distribution functions are concerned. These results apply to any dimensions including the two-dimensional case.