### 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 language | English |
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Pages (from-to) | 6973-6983 |

Number of pages | 11 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 33 |

DOIs | |

Publication status | Published - Aug 23 2002 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*35*(33), 6973-6983. https://doi.org/10.1088/0305-4470/35/33/301

**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.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 35, no. 33, pp. 6973-6983. https://doi.org/10.1088/0305-4470/35/33/301

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TY - JOUR

T1 - Optimal cooperation and submodularity for computing Potts' partition functions with a large number of states

AU - Anglès d'Auriac, J. Ch

AU - Iglói, F.

AU - Preissmann, M.

AU - Sebo, A.

PY - 2002/8/23

Y1 - 2002/8/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041381202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041381202&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/33/301

DO - 10.1088/0305-4470/35/33/301

M3 - Article

AN - SCOPUS:0041381202

VL - 35

SP - 6973

EP - 6983

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 33

ER -