Spontaneous symmetry breaking and linear effective potentials

TL;DR

This paper explains how linear effective potentials emerge from non-trivial saddle points in scalar and Yukawa models, providing insights into spontaneous symmetry breaking and the Maxwell construction.

Contribution

It offers simple derivations demonstrating the origin of linear effective potentials from saddle points in models with spontaneous symmetry breaking.

Findings

Linear effective potentials arise from dominant saddle points.

The derivations apply to scalar and Yukawa models.

Insights into the Maxwell construction and convexity of effective potentials.

Abstract

The convexity of a scalar effective potential is a well known property, and, in the situation of spontaneous symmetry breaking, leads to the so-called Maxwell construction, characterised by a flat effective potential between the minima of the bare potential. Simple derivations are given here, which show how linear effective potentials arise from non-trivial saddles points which dominate the partition function, for a self-interacting scalar field and for a Yukawa model.