Optimal Cooperation and Submodularity for Computing Potts' Partition Functions with a Large Number of State
J-Ch. Angles d'Auriac, F. Igloi, M. Preissmann, A. Sebo
Abstract
The partition function of the q-state Potts model with random ferromagnetic couplings in the large-q limit is generally dominated by the contribution of a single diagram of the high temperature expansion. Computing this dominant diagram amounts to minimizing a particular submodular function. We provide a combinatorial optimization algorithm, the optimal cooperation algorithm, which works in polynomial time for any lattice. Practical implementation and the speed of the method is also discussed.
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