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 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