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

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 $Ntoinfty$ 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.