The high temperature ising model on the triangular lattice is a critical Bernoulli percolation model

András Bálint, Federico Camia, Ronald Meester

Research output: Contribution to journalArticle

Abstract

We define a new percolation model by generalising the FK representation of the Ising model, and show that on the triangular lattice and at high temperatures, the critical point in the new model corresponds to the Ising model. Since the new model can be viewed as Bernoulli percolation on a random graph, our result makes an explicit connection between Ising percolation and critical Bernoulli percolation, and gives a new justification of the conjecture that the high temperature Ising model on the triangular lattice is in the same universality class as Bernoulli percolation.

Original languageEnglish (US)
Pages (from-to)122-138
Number of pages17
JournalJournal of Statistical Physics
Volume139
Issue number1
DOIs
StatePublished - Mar 1 2010

Fingerprint

Triangular Lattice
Bernoulli
Ising model
Ising Model
Model
Random Graphs
Ising
Justification
Universality
Critical point
critical point

Keywords

  • DaC models
  • Dependent percolation
  • Duality
  • Ising model
  • p=1/2
  • Random-cluster measures
  • Sharp phase transition

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The high temperature ising model on the triangular lattice is a critical Bernoulli percolation model. / Bálint, András; Camia, Federico; Meester, Ronald.

In: Journal of Statistical Physics, Vol. 139, No. 1, 01.03.2010, p. 122-138.

Research output: Contribution to journalArticle

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