Maxwell Construction for Scalar Field Theories with Spontaneous Symmetry Breaking

TL;DR

This paper uses a non-perturbative approach to derive the convexity and flattening of the effective potential in scalar field theories with spontaneous symmetry breaking, extending Maxwell Construction concepts.

Contribution

It explicitly derives the flattening of the effective potential in scalar theories with spontaneous symmetry breaking and generalizes Maxwell Construction to O(N) symmetric models.

Findings

Effective potential becomes flat in the infinite volume limit.

Convexity of the effective potential is proven.

Flattening does not occur in Abelian Higgs theory.

Abstract

Using a non-perturbative approximation for the partition function of a complex scalar model, which features spontaneous symmetry breaking, we explicitly derive the flattening of the effective potential in the region limited by the minima of the bare potential. This flattening occurs in the limit of infinite volume, and is a consequence of the summation over the continuous set of saddle points which dominate the partition function. We also prove the convexity of the effective potential and generalize the Maxwell Construction for scalar theories with O(N) symmetry. Finally, we discuss why the flattening of the effective potential cannot occur in the Abelian Higgs theory.