Ising models, julia sets, and similarity of the maximal entropy measures

Research output: Contribution to journalArticle

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Abstract

We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted by f) of Ĉ and that the singularities of the free energy lie on the Julia set J(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure on J(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure.

Original languageEnglish
Pages (from-to)815-825
Number of pages11
JournalJournal of Statistical Physics
Volume78
Issue number3-4
DOIs
Publication statusPublished - Feb 1 1995
Externally publishedYes

Fingerprint

Julia set
Ising model
Ising Model
Free Energy
free energy
Entropy
entropy
Logarithmic Potential
Analytic Continuation
Endomorphism
Renormalization Group
Critical Exponents
Phase Transition
exponents
Singularity
Model
Similarity
temperature

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Ising models, julia sets, and similarity of the maximal entropy measures. / Ishii, Yutaka.

In: Journal of Statistical Physics, Vol. 78, No. 3-4, 01.02.1995, p. 815-825.

Research output: Contribution to journalArticle

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