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

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

2010-05-12

arxiv.org/abs/1005.1993v1

Phys.Rev.Lett.104:251601,2010

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, 3 figs

Scientific paper

10.1103/PhysRevLett.104.251601

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.

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