Testing Scalar Field Self-Dualities in d=2 using a Variational Method

TL;DR

This paper evaluates saddle-point based self-dualities in 1+1 dimensional scalar field theories using a variational approach, finding good agreement for free energy but notable discrepancies in correlation length predictions.

Contribution

It provides a quantitative test of self-dualities in scalar field theories, highlighting their strengths and limitations in predicting phase transition properties.

Findings

Saddle-point methods agree with exact results for free energy.

Discrepancy of about 25% in correlation length peak location.

Validates the use of variational methods for certain scalar field theory predictions.

Abstract

Recently, self-dualities based on saddle-point expansions have been proposed as a means to obtain qualitative non-perturbative information in scalar field theories. In this work, we test this proposition quantitatively by studying the phase transition for critical scalar $\phi^4$ field theory in 1+1 dimensions using a variational method. We find that saddle-point methods obtain quantitative agreement for the free energy, but differ on the order of 25 percent for the peak location of the correlation length.