Towards Functional Flows for Hierarchical Models

Details Towards Functional Flows for Hierarchical Models Towards Functional Flows for Hierarchical Models

2007-04-12

arxiv.org/abs/0704.1514v2

Phys.Rev.D76:105001,2007

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 4 figures; wording sharpened, typos removed, reference added; to appear with PRD

Scientific paper

10.1103/PhysRevD.76.105001

The recursion relations of hierarchical models are studied and contrasted with functional renormalisation group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where the spectrum of universal eigenvalues at criticality is studied. A significant correlation amongst scaling exponents is pointed out and analysed in view of an underlying optimisation. Functional flows are provided which match with high accuracy all known scaling exponents from Dyson's hierarchical model for discrete block-spin transformations. Implications of the results are discussed.

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