First order phase transition with functional renormalization group method

TL;DR

This paper employs the functional renormalization group, specifically the Wegner-Houghton equation, to identify and analyze first order phase transitions in a scalar field theory, revealing complex transition behavior.

Contribution

It introduces an improved method for tracking renormalization group flow to locate phase transitions, uncovering additional radiative corrections leading to multiple transition types.

Findings

Identification of first order phase transitions using the Wegner-Houghton equation

Discovery of radiative corrections generating second order transitions

Monte-Carlo simulations faced convergence issues preventing conclusive results

Abstract

The renormalization group method, more specifically the Wegner-Houghton equation, is used to find first order phase transitions in a simple scalar field theory with a polynomial potential. An improved definition of the running parameters allows us to explore the renormalization group flow down to the IR end point and to locate phase transitions. Beyond the expected first order transition further radiative correction generated first and second order transitions are found. The phase diagram is reviewed by a Monte-Carlo simulation of the lattice regulated version of the theory but the serious slow down of the convergence prevents us to obtain conclusive results from the simulation.