Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT

Abstract

The Bethe lattice Ising model -- a classical model of statistical mechanics for the phase transition -- provides a novel and intuitive understanding of the prototypical relationship between tensor networks and Anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. After analytically formulating a holographic renormalization group for the Bethe lattice model, we demonstrate the underlying mechanism and the exact scaling dimensions for the power-law decay of boundary spin correlations by introducing the relation between the lattice network and an effective Poincare metric on a unit disk. We compare the Bethe lattice model in the high-temperature region with a scalar field in AdS${}_2$, and then discuss its more direct connection to the p-adic AdS/CFT. In addition, we find that the phase transition in the interior induces a crossover behavior of boundary spin correlations, depending on the depth of the corresponding correlation path.

15 pages, 8 figures

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• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
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Cited by in corpus (6)

• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models
• Finite Temperature at Finite Places
• Vertex Representation of Hyperbolic Tensor Networks
• A glimpse into the Ultrametric spectrum
• Holographic Aspects of Dynamical Mean-Field Theory