Local Spontaneous Symmetry Breaking for Film System Within Scalar $\phi^4$ Model for Phase Transition

TL;DR

This paper investigates how local spontaneous symmetry breaking influences phase transitions in finite-size film systems modeled by a scalar ^4 theory, emphasizing the importance of vacuum states and boundary conditions.

Contribution

It introduces an approximate method to analyze non-trivial vacuum states and demonstrates the significance of spontaneous symmetry breaking in perturbative calculations for film systems.

Findings

Spontaneous symmetry breaking is crucial for understanding phase transitions in finite systems.

Vacuum states vary with boundary conditions and affect fluctuation evaluations.

Perturbative calculations are valid when local symmetry breaking effects are considered.

Abstract

The difficulty is analysed in evaluating fluctuations in phase transition of finite-size system at temperature far below the critical point. Film system is discussed with one-component order parameter $\phi^4$ model for phase transition. Non-trivial vacuum state corresponding to minimum Hamiltonian is given approximately for various boundary conditions. It is shown that the spontaneous symmetry breaking plays an important role for such systems, and that perturbative calculations can be done safely when the effect of the vacuum state or the local spontaneous symmetry breaking is taken into consideration.