Absolute continuity of non-homogeneous Gibbs measures of the Ising model on the Cayley tree

Farrukh Mukhamedov, Otabek Khakimov

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, for the Ising model on the Cayley tree of order k ⩾ 2 , a sequence { h n } of boundary conditions is constructed depending on an initial value h which defines a Gibbs measure µ h . By investigating the dynamical behaviour of the renormalisation group map associated with the model, we prove that each measure µ h is equivalent to the disordered phase μ ∗ . This result shines a new light to the question closely related to the classical result by Kakutani which asserts that any two locally-equivalent probability product measures are either equivalent or mutually-singular.

Original languageEnglish
JournalNonlinearity
Volume36
Issue number10
DOIs
Publication statusPublished - Oct 1 2023

Keywords

  • 39A70
  • 46S10
  • 47H10
  • 60K35
  • 82B26
  • absolute continuity
  • Cayley tree
  • disordered phase
  • Gibbs measure
  • Ising model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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