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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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
Online AccessGet full text
ISSN2050-3911
2050-3911
DOI10.1093/ptep/ptad156

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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 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.
AbstractList 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.
Author Takayanagi, Tadashi
Okunishi, Kouichi
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  fullname: Takayanagi, Tadashi
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CitedBy_id crossref_primary_10_1093_ptep_ptae137
crossref_primary_10_1103_PhysRevE_111_024105
crossref_primary_10_1007_JHEP03_2025_097
crossref_primary_10_7566_JPSJ_93_094001
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Snippet The Bethe lattice Ising model—a classical model of statistical mechanics for the phase transition—provides a novel and intuitive understanding of the...
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SubjectTerms Condensed matter physics
Critical phenomena
Phase transitions
Physics
Spacetime
Statistical mechanics
Theoretical physics
Title Statistical mechanics approach to the holographic renormalization group: Bethe lattice Ising model and p-adic AdS/CFT
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