Sharp Phase Transition for the Random-Cluster Model with Summable External Magnetic Field

Abstract

In this paper, we prove sharpness of the phase transition for the random-cluster model in summable positive external fields, with cluster weight q=2,3,..., on the hypercubic lattice. That is, there exists some nontrivial critical parameter that depends on the cluster weight and the external field, below which the model exhibits exponential decay and above which there exists almost surely an infinite cluster.

arXiv comment17 pages. Accepted for publication in Markov Process And Related Fields

References in corpus (5)

• The Random-Cluster Model
• Graphical Representations for Ising Systems in External Fields
• Graphical Representations for Ising and Potts Models in General External Fields
• Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields
• The phase transitions of the random-cluster and Potts models on slabs with $q\ge 1$ are sharp