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

András Bálint; Federico Camia; Ronald Meester

doi:10.1007/s10955-010-9930-y

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

András Bálint, Federico Camia, Ronald Meester

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	122-138
Number of pages	17
Journal	Journal of Statistical Physics
Volume	139
Issue number	1
DOIs	https://doi.org/10.1007/s10955-010-9930-y
State	Published - 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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10.1007/s10955-010-9930-y

Cite this

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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.",

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

author = "Andr{\'a}s B{\'a}lint and Federico Camia and Ronald Meester",

note = "Funding Information: The research of Federico Camia has been supported in part by a Veni grant of the NWO (Dutch Organisation for Scientific Research), and the research of Ronald Meester has been supported in part by a Vici grant of the NWO.",

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AU - Bálint, András

AU - Camia, Federico

AU - Meester, Ronald

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N2 - 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.

AB - 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.

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KW - Dependent percolation

KW - Duality

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KW - Random-cluster measures

KW - Sharp phase transition

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

Abstract

Keywords

ASJC Scopus subject areas

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