Fisher's zeros as boundary of renormalization group flows in complex coupling spaces

Abstract

We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that the Fisher's zeros are located at the boundary of the complex basin of attraction of infra-red fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of 4-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action, stabilize at a distance larger than 0.15 from the real axis in the complex beta=4/g^2 plane. We discuss the implications for proofs of confinement and searches for nontrivial infra-red fixed points in models beyond the standard model.

4 pages, 3 figs

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• Measuring complex partition function zeroes of Ising models in quantum simulators
• Complex RG flows for 2D nonlinear O(N) sigma models
• Lines of Fisher's zeros as separatrices for complex renormalization group flows
• New applications of the renormalization group method in physics -- a brief introduction
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Signatures of quantum criticality in the complex inverse temperature plane
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Complex singularities around the QCD critical point at finite densities
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Detecting Many-Body Scars from Fisher Zeros
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• Fisher's zeros as boundary of RG flows in complex coupling space
• Fisher's zeros, complex RG flows and confinement in LGT models