Absence of second order phase transition in $ \lambda \phi^4$ theory

TL;DR

This paper investigates the finite-temperature behavior of scalar λφ^4 theory and concludes that it does not exhibit a second order phase transition, based on calculations of self-energy and renormalization group analysis.

Contribution

The study provides a novel analysis showing the absence of second order phase transitions in λφ^4 theory using a modified perturbation expansion and renormalization group techniques.

Findings

No second order phase transition occurs in λφ^4 theory.

Infrared freedom leads to the critical temperature equation being satisfied at all temperatures.

Modified perturbation expansion effectively analyzes finite-temperature effects.

Abstract

We calculate the self-energy at finite temperature in scalar $\lambda\phi ^4$ theory to second order in a modified perturbation expansion. Using the renormalisation group equation to tame the logarithms in momentum, it gives an equation to determine the critical temperature. Due to the infrared freedom of the theory, this equation is satisfied, irrespective of the value of the temperature. We conclude that there is no second order phase transition in this theory.