Asymptotically Free Theory with Scale Invariant Thermodynamics

TL;DR

This paper applies a novel variational resummation technique to a two-dimensional nonlinear sigma model, demonstrating that nonperturbative thermodynamic results with scale invariance can be obtained efficiently, sharing features with Yang-Mills theories.

Contribution

It introduces a renormalization group consistent variational resummation method to evaluate thermodynamics in models with asymptotic freedom, confirming nonperturbative results from lowest-order approximations.

Findings

Nonperturbative thermodynamics can be derived from lowest-order quasi-particle contributions.

Next-to-leading corrections improve convergence and preserve scale invariance.

Method successfully reproduces features like asymptotic freedom and trace anomaly.

Abstract

A recently developed variational resummation technique, incorporating renormalization group properties consistently, 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, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasi-particle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.