On the ratio of string tensions in the 3D Z_4 lattice gauge theory

TL;DR

This paper demonstrates that in a 3D Z_4 lattice gauge theory, the ratios of k-string tensions remain constant throughout the entire confining phase, supported by numerical and analytical methods.

Contribution

It shows that the ratios of string tensions are constant in the whole confining phase of the 3D Z_4 gauge model, extending previous partial results.

Findings

Ratios of k-string tensions are constant in the confining phase.

Numerical experiments support the constancy of tension ratios.

Exact results from an integrable spin model corroborate the findings.

Abstract

It was recently pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.