Abstract
For the unbounded spin systems one cannot get cluster expansion if there exist large enough boundary values. A simple idea to avoid these difficulties is to prove that with probabilityp Λ→ 1 when Λ↑ℤv there is a large subvolume Λ′ of Λ such that on ∂Λ′ all spin values do not exceed some fixed number. This gives a new method to prove uniqueness results for the unbounded spin systems generalizing some results of Refs. 1 and 2. The formulations of these results are in Section 1; the proofs are in Section 2.
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References
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Malyshev, V.A., Nickolaev, I.V. Uniqueness of gibbs fields via cluster expansions. J Stat Phys 35, 375–379 (1984). https://doi.org/10.1007/BF01014390
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DOI: https://doi.org/10.1007/BF01014390