Functional renormalization group approach to the Yang-Lee edge singularity

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 $3\le d\le 6$ 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.

10 pages, 4 figures, updated reference to supplementary material