Approximate ground states of the random-field Potts model from graph cuts

Manoj Kumar, Ravinder Kumar, Martin Weigel, Varsha Banerjee, Wolfhard Janke, Sanjay Puri

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    Abstract

    While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number
    q
    of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.
    Original languageEnglish
    Article number053307
    Pages (from-to)1-10
    Number of pages10
    JournalPhysical review E: Statistical, Nonlinear, and Soft Matter Physics
    Volume97
    Issue number5
    DOIs
    Publication statusPublished - 14 May 2018

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