Universal location of the Yang-Lee edge singularity in O(N) theories

TL;DR

This paper identifies a universal point called the Yang-Lee edge singularity in O(N) theories across various N and dimensions, using the functional renormalization group to explore nonperturbative physics.

Contribution

It determines the universal location of the Yang-Lee edge singularity for O(N) theories across different N and dimensions, including large N and mean-field limits, using the functional renormalization group.

Findings

Reproduces the N→∞ analytical result for the singularity location.

Obtains the mean-field result in 4 dimensions.

Provides a nonperturbative analysis for arbitrary N, d, and complex external fields.

Abstract

We determine a previously unknown universal quantity, the location of the Yang-Lee edge singularity for the O($N$) theories in a wide range of $N$ and various dimensions. At large $N$, we reproduce the $N\to\infty$ analytical result on the location of the singularity and, additionally, we obtain the mean-field result for the location in $d=4$ dimensions. In order to capture the nonperturbative physics for arbitrary $N$, $d$ and complex-valued external fields, we use the functional renormalization group approach.