Lee-Yang model from the functional renormalization group

TL;DR

This paper uses the functional renormalization group to analyze the critical properties of the Lee-Yang model in less than six dimensions, providing estimates for critical exponents and exploring scheme dependence and convergence.

Contribution

It introduces a truncation-based method to study the Lee-Yang model's critical behavior across multiple dimensions, including a qualitative analysis in 2 and 3 dimensions.

Findings

Estimated critical exponents in 4 and 5 dimensions.

Demonstrated convergence of results with increasing truncation size.

Proposed existence of additional nonunitary multicritical theories.

Abstract

We investigate the critical properties of the Lee-Yang model in less than six spacetime dimensions using truncations of the functional renormalization group flow. We give estimates for the critical exponents, study the dependence on the regularization scheme, and show the convergence of our results for increasing size of the truncations in four and five dimensions. While with our truncations it is numerically challenging to approach the three-dimensional case, we provide a simple approximation which allows us to qualitatively study the Lee-Yang model in two and three dimensions, and use it to argue the existence of further nonunitary multicritical theories including one which is relevant for the universality class of the Blume-Capel model.