Possibility of the new type phase transition

TL;DR

This paper investigates how boundary conditions in scalar field theories can induce a new type of phase transition, influenced by temperature and system size, leading to phenomena like spontaneous symmetry breaking and Higgs model emergence.

Contribution

It introduces a novel phase transition mechanism driven by boundary conditions, expanding understanding of symmetry breaking in scalar field theories.

Findings

Dirichlet boundary conditions cause spontaneous symmetry breaking.

A new phase transition occurs due to boundary effects and temperature-size competition.

Massless scalar electrodynamics can evolve into the Higgs model.

Abstract

The scalar field theory and the scalar electrodynamics quantized in the flat gap are considered. The dynamical effects arising due to the boundary presence with two types of boundary conditions (BC) satisfied by scalar fields are studied. It is shown that while the Neumann BC lead to the usual scalar field mass generation, the Dirichlet BC give rise to the dynamical mechanism of spontaneous symmetry breaking. Due to the later, there arises the possibility of the new type phase transition from the normal to spontaneously broken phase. The decreasing in the characteristic size of the quantization region (the gap size here) and increasing in the temperature compete with each other, tending to transport the system in the spontaneously broken and in the normal phase, respectively. The system evolves with a combined parameter, simultaneously reflecting the change in temperature and in the size. As a result, at the critical value of this parameter there occurs the phase transition from the normal phase to the spontaneously broken one. In particular, the usual massless scalar electrodynamics transforms to the Higgs model.