Six loop critical exponent analysis for Lee-Yang and percolation theory

TL;DR

The paper advances the study of critical phenomena for Lee-Yang edge singularities and percolation by exploiting the six-loop renormalization-group functions of a scalar cubic theory to obtain $\epsilon$-expansions around $d=6-\epsilon$. It deploys constrained two-sided Padé approximants, anchored by exact low-dimensional results at $d=2$ (and $d=1$ when available), to extract estimates in $d=3,4,5$ and to quantify uncertainties. The authors provide six-loop expansions for a broad set of exponents, report new numerical estimates in $d=3,4,5$, and show consistency with other theoretical approaches such as conformal bootstrap and functional RG. This demonstrates the robustness and competitiveness of high-loop perturbative methods for cubic scalar theories and enriches the cross-method validation of Lee-Yang and percolation critical data.

Abstract

Using the recent six loop renormalization group functions for Lee-Yang and percolation theory constructed by Schnetz from a scalar cubic Lagrangian, we deduce the $ε$ expansion of the critical exponents for both cases. Estimates for the exponents in three, four and five dimensions are extracted using two-sided Padé approximants and shown to be compatible with values from other approaches.