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

• URL: http://arxiv.org/abs/2310.12601v1
• Date: Thu, 19 Oct 2023 09:14:03 GMT
• Title: Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Authors: Kouichi Okunishi and Tadashi Takayanagi
• Abstract summary: The Bethe lattice Ising model is a classical model of statistical mechanics for the phase transition. We show the underlying mechanism and the exact scaling dimensions for the power-law decay of boundary spin correlations. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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