Scalar Field Theory at Finite Temperature in D=2+1

TL;DR

This paper investigates the $^6$ scalar field theory in 2+1 dimensions at finite temperature, employing the 1/N expansion and CJT method to analyze phase behavior and confirm the Coleman-Mermin-Wagner theorem.

Contribution

It applies the 1/N expansion and CJT formalism to finite-temperature scalar field theory in 2+1 dimensions, explicitly demonstrating the Coleman-Mermin-Wagner theorem.

Findings

Explicit demonstration of the Coleman-Mermin-Wagner theorem at finite temperature.

Use of 1/N expansion and CJT method to sum Feynman graphs.

Analysis of phase behavior in scalar field theory at finite temperature.

Abstract

We discuss the $\phi^6 $ theory defined in $D=2+1$-dimensional space-time and assume that the system is in equilibrium with a thermal bath at temperature $\beta^{-1}$. We use the $ 1/N $ expansion and the method of the composite operator (CJT) for summing a large set of Feynman graphs.We demonstrate explicitly the Coleman-Mermin-Wagner theorem at finite temperature.