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.

arXiv comment10 pages, 4 figures, updated reference to supplementary material

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• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Lee-Yang model from the functional renormalization group
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• On spinodal points and Lee-Yang edge singularities
• A functional perspective on emergent supersymmetry
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Functional flows for complex effective actions
• Operator product expansion coefficients in the exact renormalization group formalism
• Uniformizing Lee-Yang Singularities
• Lee-Yang and Langer edge singularities from analytic continuation of scaling functions
• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Tunable tachyon mass in the PT-broken massive Thirring model
• Universality, Lee-Yang singularities and series expansions
• Critical and multicritical Lee-Yang fixed points in the local potential approximation