Finite size effects in the phase transition patterns of coupled scalar field systems

TL;DR

This paper investigates how finite size and temperature influence phase transition patterns in a coupled two-scalar field system, revealing effects like reentrant phase transitions and critical temperature shifts.

Contribution

It introduces a detailed analysis of finite size effects on phase transitions in coupled scalar fields, including boundary conditions and temperature variations, which is a novel extension of previous models.

Findings

Finite size affects critical temperature for symmetry restoration.

Reentrant phase transition behavior observed with varying size L.

Finite temperature and size interplay influences phase transition patterns.

Abstract

It is considered in this work the phase transition patterns for a coupled two-scalar field system model under the combined effects of finite sizes and temperature. The scalar fields are taken as propagating in a D=4 Euclidean space with the usual periodic compactification in the Euclidean time direction (with dimension given by the inverse of the temperature) and also under a compact dimension in the space direction, which is restricted to size L. In the latter case, a Dirichlet boundary condition is considered. Finite-size variation of the critical temperature for the cases of symmetry restoration and inverse symmetry breaking are studied. At fixed finite-temperature values, the variation of the inverse correlation lengths with the size L might display a behavior analogous to reentrant phase transitions. Possible applications of our results to physical systems of interest are also discussed.