Optimal cooperation and submodularity for computing Potts' partition functions with a large number of states

J. Ch Anglès d'Auriac, F. Iglói, M. Preissmann, A. Sebo

Research output: Contribution to journalArticle

27 Citations (Scopus)

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. The implementation of the method and its running time are also discussed.

Original languageEnglish
Pages (from-to)6973-6983
Number of pages11
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number33
DOIs
Publication statusPublished - Aug 23 2002

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Submodularity
Partition Function
partitions
Diagram
diagrams
Potts model
High Temperature Expansion
Submodular Function
Combinatorial Algorithms
Computing
Combinatorial optimization
Combinatorial Optimization
Potts Model
Optimization Algorithm
Polynomial time
polynomials
Polynomials
optimization
expansion
Temperature

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Optimal cooperation and submodularity for computing Potts' partition functions with a large number of states. / Anglès d'Auriac, J. Ch; Iglói, F.; Preissmann, M.; Sebo, A.

In: Journal of Physics A: Mathematical and General, Vol. 35, No. 33, 23.08.2002, p. 6973-6983.

Research output: Contribution to journalArticle

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