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Representation and Poly-time Approximation for Pressure of \(\mathbb {Z}^2\) Lattice Models in the Non-uniqueness Region

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Abstract

We develop a new pressure representation theorem for nearest-neighbour Gibbs interactions and apply this to obtain the existence of efficient algorithms for approximating the pressure in the 2-dimensional ferromagnetic Potts, multi-type Widom–Rowlinson and hard-core models. For Potts model, our results apply to every inverse temperature but the critical. For Widom–Rowlinson and hard-core models, they apply to certain subsets of both the subcritical and supercritical regions. The main novelty of our work is in the latter.

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Acknowledgments

We thank Nishant Chandgotia and Andrew Rechnitzer for helpful discussions. We also thank the anonymous referees. B. Marcus was partially supported by an NSERC grant and R. Pavlov was partially supported by an NSF grant.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, UK

    Stefan Adams

  2. Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Raimundo Briceño & Brian Marcus

  3. Department of Mathematics, University of Denver, 2280 S. Vine St., Denver, CO, 80208, USA

    Ronnie Pavlov

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  1. Stefan Adams
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  2. Raimundo Briceño
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  3. Brian Marcus
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  4. Ronnie Pavlov
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Correspondence to Raimundo Briceño.

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Adams, S., Briceño, R., Marcus, B. et al. Representation and Poly-time Approximation for Pressure of \(\mathbb {Z}^2\) Lattice Models in the Non-uniqueness Region. J Stat Phys 162, 1031–1067 (2016). https://doi.org/10.1007/s10955-015-1433-4

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