Abstract
We consider the Fortuin-Kasteleyn cluster model which is related to the percolation model and the Potts model. We give the asymptotic behavior of the critical probability and the percolation probability as the dimension d tends to infinity, in the case where Q (which corresponds to the number of colors in the Potts model) lies between 1 and 2.
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Kesten, H. (1991). Asymptotics in High Dimensions For the Fortuin-Kasteleyn Random Cluster Model. In: Alexander, K.S., Watkins, J.C. (eds) Spatial Stochastic Processes. Progress in Probability, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0451-0_4
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DOI: https://doi.org/10.1007/978-1-4612-0451-0_4
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