Towards Functional Flows for Hierarchical Models

Abstract

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.

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

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• The nonperturbative functional renormalization group and its applications
• Further evidence for asymptotic safety of quantum gravity
• One force to rule them all: asymptotic safety of gravity with matter
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Ising exponents from the functional renormalisation group
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Global Wilson-Fisher fixed points
• Fixed points and the spontaneous breaking of scale invariance
• Asymptotic safety of scalar field theories
• Error estimates and specification parameters for functional renormalization
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group
• Functional renormalization flow and dynamical chiral symmetry breaking of QCD
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• One-dimensional long-range Ising model: two (almost) equivalent approximations