Statistical mechanics approach to the holographic renormalization group: Bethe lattice Ising model and p-adic AdS/CFT

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 the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. After analytically formula...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2024; no. 1
Main Authors Okunishi, Kouichi, Takayanagi, Tadashi
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.01.2024
Subjects
Condensed matter physics
Critical phenomena
Phase transitions
Physics
Spacetime
Statistical mechanics
Theoretical physics
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ISSN2050-3911
2050-3911
DOI10.1093/ptep/ptad156

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Summary: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 the 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 Poincaré metric on a unit disk. We compare the Bethe lattice model in the high-temperature region with a scalar field in AdS2, 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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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptad156