Functional renormalization group approach to the Yang-Lee edge singularity

TL;DR

This paper uses a nonperturbative functional renormalization group approach to analyze the critical behavior of the Yang-Lee edge singularity across dimensions 3 to 6, achieving good agreement with existing data and methods.

Contribution

It applies the functional renormalization group to the Yang-Lee edge singularity, providing new insights and accurate estimates of critical exponents in various dimensions.

Findings

Excellent agreement with high-temperature series data in 3D

Consistent results with four-loop epsilon expansion

Estimated errors from truncation of effective action

Abstract

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in $3 \leq d\leq 6$ Euclidean dimensions. We find very good agreement with high-temperature series data in $d = 3$ dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop $\epsilon = 6-d$ expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG $\beta$ functions is discussed and we estimate the error associated with $\mathcal{O}(\partial^4)$ truncations of the scale-dependent effective action.