Symmetry breaking in nonuniform noncommutative $\lambda\phi^4$ theory at finite temperature

TL;DR

This paper investigates how noncommutative scalar field theories at finite temperature exhibit symmetry breaking and phase transitions, revealing new anisotropic nonuniform solutions and a first-order transition between phases.

Contribution

It introduces the analysis of nonuniform, stripe-like solutions in noncommutative bb^4 theory at finite temperature, including nonplanar effects and anisotropic regions.

Findings

Nonuniform solutions appear in both planar and noncommutative cases.

The phase transition from uniform to nonuniform phase is first order.

New anisotropic nonuniform solutions are identified.

Abstract

We consider the 2PI Cornwall-Jackiw-Tomboulis effective action at finite temperature for a noncommutative real scalar field theory in 4 dimensions, with noncommutativity among space and time variables. By means of a Rayleig-Ritz variation, we study the solutions of a stripe type nonuniform background, which depends on space and time, and hence on temperature. The analysis in the first approximation shows that such solutions appear in the planar limit, as already known, but also under normal noncommutativity, in an anisotropic region which has not been considered. Further we show that the transition from the uniform ordered phase to the non uniform one is first order.