Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d \le 4$

Abstract

We determine the universal location of the Yang-Lee edge singularity in the entire relevant domain of spatial dimensions 1 ≤ d ≤ 4 for the Ising universality class. To that end, we present analytical results for d = 1, 2, 4 and near four dimensions. For d = 3 and a set of fractional dimensions, we perform numerical calculations using a systematic Functional Renormalization Group approach.

Phase Transitions in Particle Physics

“…If it can be established that the scaling behavior follows the one expected for the QCD critical point, the location of the QCD critical point can be determined by a scaling analysis. This method has been successfully applied in the Gross-Neveu model [212], see also [213] for further investigations in low energy EFTs with and without fluctuations see [214,213,215,216,217]. In particular, the scaling behavior of the location of the edge singularity has been established in [214,215,216] It is thus important to understand that these studies not only highlight different numerical strategies to calculate observables at nonvanishing chemical potential via a re-summation of the Taylor series and thus might enhance the results presented in the Section on fluctuations.…”

“…This method has been successfully applied in the Gross-Neveu model [212], see also [213] for further investigations in low energy EFTs with and without fluctuations see [214,213,215,216,217]. In particular, the scaling behavior of the location of the edge singularity has been established in [214,215,216] It is thus important to understand that these studies not only highlight different numerical strategies to calculate observables at nonvanishing chemical potential via a re-summation of the Taylor series and thus might enhance the results presented in the Section on fluctuations. They also provide, and that is what we have focused on here, a mechanism to locate the elusive QCD critical point (which has been mentioned at the beginning, and will be further discussed in the Section devoted to conformal theories.…”