Phase transition in multicomponent field theory at finite temperature

TL;DR

This paper introduces a novel approach combining optimized perturbation and self-similar approximation theories to analyze phase transitions in multicomponent field theories at finite temperature, providing accurate results without small parameters.

Contribution

It presents a new method for studying phase transitions in complex systems without relying on small parameters, validated by gauge symmetry breaking examples.

Findings

Critical indices match Monte Carlo simulations.

Approach yields exact results for known cases.

Simplifies analysis compared to traditional methods.

Abstract

Nuclear matter at finite temperature and barion density exhibits several phase transitions that could happen at the early stages of the Universe evolution and could be realized in heavy-ion or hadron-hadron collisions. Microscopic description of phase transitions is notoriously difficult because of the absence of small parameters. Here we present a general approach allowing to treat situations, when there are no small parameters. The approach is based on optimized perturbation theory and self-similar approximation theory. It allows, starting with divergent perturbation series in powers of an asymptotically small parameter, to construct expressions extrapolating asymptotic series to arbitrary values of the parameter, including its infinite limit. Examples of such approximants are: right root approximants, left root approximants, continued root approximants, exponential approximants, and factor approximants. The approach is illustrated by the phase transition of gauge symmetry breaking in a multicomponent field theory. The found critical indices are in very good agreement with Monte Carlo simulations as well as with complicated methods of Pade-Borel summation, while our approach is much simpler. The nice feature of the approach is that it gives exact values for the cases where exact solutions are known.