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- W2950342989 abstract "The Ising model at inverse temperature $beta$ and zero external field can be obtained via the Fortuin-Kasteleyn (FK) random-cluster model with $q=2$ and density of open edges $p=1-e^{-beta}$ by assigning spin +1 or -1 to each vertex in such a way that (1) all the vertices in the same FK cluster get the same spin and (2) +1 and -1 have equal probability. We generalize the above procedure by assigning spin +1 with probability $r$ and -1 with probability $1-r$, with $r in [0,1]$, while keeping condition (1). For fixed $beta$, this generates a dependent (spin) percolation model with parameter $r$. We show that, on the triangular lattice and for $beta 1/2$, sharpness of the percolation phase transition (by showing exponential decay of the cluster size distribution for $r<1/2$), and continuity of the percolation function for all $r in [0,1]$." @default.
- W2950342989 created "2019-06-27" @default.
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- W2950342989 date "2008-06-18" @default.
- W2950342989 modified "2023-09-23" @default.
- W2950342989 title "The high temperature Ising model on the triangular lattice is a critical percolation model" @default.
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