Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory

TL;DR

This paper applies the smooth cutoff hierarchical reference theory to the three-dimensional phi4 scalar field model, successfully capturing phase transition behaviors and critical phenomena consistent with the Ising universality class.

Contribution

It introduces a smooth cutoff formulation of HRT that accurately describes both first and second order phase transitions in phi4 field theory.

Findings

Critical exponents match Ising universality class

Inverse susceptibility vanishes inside coexistence curve

Discontinuity across phase boundary confirmed

Abstract

The phi4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.