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

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