Optimal Cooperation and Submodularity for Computing Potts' Partition Functions with a Large Number of State

Details Optimal Cooperation and Submodularity for Computing Potts' Partition Functions with a Large Number of State Optimal Cooperation and Submodularity for Computing Potts' Partition Functions with a Large Number of State

2002-04-02

arxiv.org/abs/cond-mat/0204055v1

Physics

Condensed Matter

Statistical Mechanics

18 pages, no figure

Scientific paper

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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