Virial expansion and TBA in O(N) sigma models

TL;DR

This paper analyzes the free energy of 1+1 dimensional O(N) sigma models for even N using TBA equations, deriving explicit solutions, virial coefficients, and comparing results to large N approximations.

Contribution

The paper provides explicit formulas for the TBA Y-system solutions and calculates the first two virial coefficients for the models.

Findings

Explicit solutions for the TBA Y-system are derived.

First two virial coefficients are calculated.

Comparison with large N results shows consistency.

Abstract

We study the free energy of the 1+1 dimensional O(N) nonlinear sigma-models for even N using the TBA equations proposed recently. We give explicit formulae for the constant solution of the TBA equations (Y-system) and calculate the first two virial coefficients. The free energy is also compared to the leading large N result.