Scale independence in an asymptotically free theory at finite temperatures

TL;DR

This paper applies a variational resummation technique that respects renormalization group properties to study thermodynamics in a two-dimensional nonlinear sigma model, revealing scale invariance and nonperturbative effects.

Contribution

It demonstrates the effectiveness of a renormalization group-based variational method in achieving scale independence and nonperturbative insights in a model with features similar to Yang-Mills theories.

Findings

Nonperturbative results obtained from lowest-order calculations.

Next-to-leading correction suggests convergence to scale invariance.

Method applicable to theories with asymptotic freedom and trace anomaly.

Abstract

A recently developed variational resummation technique incorporating renormalization group properties has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. Besides the fact that nonperturbative results can be readily generated solely by considering the lowest-order contribution to the thermodynamic effective potential, we also show that its next-to-leading correction indicates convergence to the sought-after scale invariance.