A non-perturbative analysis of symmetry breaking in two-dimensional phi^4 theory using periodic field methods

TL;DR

This paper extends spherical field theory to periodic field methods, applying it to two-dimensional phi^4 theory to compute critical parameters and compare with lattice and Ising model results.

Contribution

It introduces a periodic-box mode expansion for spherical field theory and applies it to analyze symmetry breaking in 2D phi^4 theory.

Findings

Calculated critical coupling and exponents for 2D phi^4 theory.

Results agree with lattice and Ising model predictions.

Demonstrated the effectiveness of periodic field methods.

Abstract

We describe the generalization of spherical field theory to other modal expansion methods. The main approach remains the same, to reduce a d-dimensional field theory into a set of coupled one-dimensional systems. The method we discuss here uses an expansion with respect to periodic-box modes. We apply the method to phi^4 theory in two dimensions and compute the critical coupling and critical exponents. We compare with lattice results and predictions via universality and the two-dimensional Ising model.