First-order phase transitions in confined systems

TL;DR

This paper investigates how the transition temperature in a confined Euclidean field-theoretical model depends on the separation between boundaries, revealing a concave relationship and a minimal separation for phase transition suppression.

Contribution

It provides a detailed analysis of the dependence of transition temperature on confinement size in a $(^4+^6)_D$ model, including the identification of a minimal separation for phase transition.

Findings

Transition temperature $T_c$ is a concave function of inverse separation $L^{-1}$.

There exists a minimal separation below which the phase transition is suppressed.

The study extends understanding of phase transitions in confined geometries.

Abstract

In a field-theoretical context, we consider the Euclidean $(\phi^4+\phi^6)_D$ model compactified in one of the spatial dimensions. We are able to determine the dependence of the transition temperature ($T_{c}$)for a system described by this model, confined between two parallel planes, as a function of the distance($L$) separating them. We show that $T_{c}$ is a concave function of $L^{-1}$. We determine a minimal separation below which the transition is suppressed.