Convexity at finite temperature and non-extensive thermodynamics

TL;DR

This paper explores the effects of finite volume and temperature on the effective potential in scalar field theories, revealing that convexity and symmetry breaking depend on volume and thermal conditions, with implications for ultra-light particles.

Contribution

It provides a new derivation of the effective potential considering tunneling between minima at finite volume, highlighting non-extensive thermodynamics effects.

Findings

Convexity requires including both minima in the path integral.

Effective potential is volume-suppressed and lacks spontaneous symmetry breaking at finite volume.

Finite temperature introduces non-extensive free energy properties.

Abstract

Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two bare minima are taken into account in the path integral, and a new derivation of the effective potential is given, in the large volume limit. The effective potential has then has a universal form, it is suppressed by the space time volume, and does not feature spontaneous symmetry breaking as long as the volume is finite. The finite temperature analysis leads to surprising thermal properties, following from the non-extensive expression for the free energy. Although the physical relevance of these results is not clear, the potential application to ultra-light scalar particles is discussed.