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 journalArticlepeer-review

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 2010

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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