### 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) |
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Pages (from-to) | 122-138 |

Number of pages | 17 |

Journal | Journal of Statistical Physics |

Volume | 139 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2010 |

### Fingerprint

### 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

*Journal of Statistical Physics*,

*139*(1), 122-138. https://doi.org/10.1007/s10955-010-9930-y

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 139, no. 1, pp. 122-138. https://doi.org/10.1007/s10955-010-9930-y

}

TY - JOUR

T1 - The high temperature ising model on the triangular lattice is a critical Bernoulli percolation model

AU - Bálint, András

AU - Camia, Federico

AU - Meester, Ronald

PY - 2010/3/1

Y1 - 2010/3/1

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.

KW - DaC models

KW - Dependent percolation

KW - Duality

KW - Ising model

KW - p=1/2

KW - Random-cluster measures

KW - Sharp phase transition

UR - http://www.scopus.com/inward/record.url?scp=77949567990&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949567990&partnerID=8YFLogxK

U2 - 10.1007/s10955-010-9930-y

DO - 10.1007/s10955-010-9930-y

M3 - Article

VL - 139

SP - 122

EP - 138

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -