Non-perturbative approach to the effective potential of the $\lambda\phi^{4} theory at finite temperature

TL;DR

This paper develops a non-perturbative method to analyze the phase structure of the $^{4}$ scalar field theory at finite temperature, revealing a second-order phase transition and consistent critical exponents.

Contribution

The paper introduces a novel non-perturbative approach using a differential equation for the effective potential, enabling numerical solutions at finite temperature.

Findings

Phase transition is of second order.

Critical exponents match Landau approximation results.

Effective potential obtained non-perturbatively.

Abstract

We construct a non-perturbative method to investigate the phase structure of the scalar theory at finite temperature. The derivative of the effective potential with respect to the mass square is expressed in terms of the full propagator. Under a certain approximation this expression reduces to the partial differential equation for the effective potential. We numerically solve the partial differential equation and obtain the effective potential non-perturbatively. It is found that the phase transition is of the second order. The critical exponents calculated in this method are consistent with the results obtained in Landau approximation.