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Lee–Yang Polynomials and Ground States of Spin Systems

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Abstract

We obtain two kinds of results on the region in the space of the interactions of lattice systems where the Lee–Yang property holds (LY domain). First we show that the LY domain is related to interactions with exactly two ground states. Then we give a description of the full LY domain of an extended “plaquette model” analyzed by Lebowitz and Ruelle (Commun Math Phys 304:711–722, 2011). This allows us to prove a permanence property of the system, which we conjecture to hold in general.

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Authors and Affiliations

  1. Physics Department, Virginia Tech, Blacksburg, USA

    Joseph Slawny

  2. Department of Physics, Technion, Haifa, Israel

    Joseph Slawny

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  1. Joseph Slawny
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Correspondence to Joseph Slawny.

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Communicated by H. Spohn

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Slawny, J. Lee–Yang Polynomials and Ground States of Spin Systems. Commun. Math. Phys. 329, 959–977 (2014). https://doi.org/10.1007/s00220-014-1910-7

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  • DOI: https://doi.org/10.1007/s00220-014-1910-7

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