Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results

TL;DR

This paper compares analytical and lattice approaches to study the thermodynamics of the 1+1 dimensional O(3) model, revealing good agreement at low temperatures and improved accuracy at high temperatures with two-loop calculations.

Contribution

It provides a detailed comparison between nonperturbative lattice simulations and analytical CJT formalism results for the O(3) model's thermodynamics.

Findings

Good agreement between CJT and lattice results at low T.

Two-loop calculations improve high T accuracy.

Pressure and energy density resemble four-dimensional Yang-Mills theories.

Abstract

A detailed study of the thermodynamics of the O(N=3) model in 1+1 dimensions is presented, employing a two-particle-irreducible resummation prescription as well as fully nonperturbative finite-temperature lattice simulations. The analytical results are computed using the Cornwall-Jackiw-Tomboulis (CJT) formalism and the auxiliary field method to one- and to two-loop order. The lattice results are obtained through Monte Carlo simulation for various lattice spacings. The analytical and lattice results for pressure, trace anomaly, and energy density, resembling closely those of four-dimensional Yang-Mills theories, are compared with each other. We find that to one-loop order there is a good correspondence between the CJT formalism and the lattice study for low temperatures. However, at high T the two-loop calculation fares better, correcting for the overestimation from the former approximation.