Abstract
In this note we consider long-range q-states Potts models on Z d, d≥ 2. For various families of non-summable ferromagnetic pair potentials φ(x)≥ 0, we show that there exists, for all inverse temperature β > 0, an integer N such that the truncated model, in which all interactions between spins at distance larger than N are suppressed, has at least q distinct infinite-volume Gibbs states. This holds, in particular, for all potentials whose asymptotic behaviour is of the type φ(x)∼ ‖x‖−α, 0≤α≤ d. These results are obtained using simple percolation arguments.
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Work supported by Swiss National Foundation for Science, Conselho Nacional de Desenvolvimento Cientìfico e Tecnològico, and Programa de Auxìlio para Recèm Doutores PRPq-UFMG.
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Friedli, S., de Lima, B.N.B. On the Truncation of Systems with Non-Summable Interactions. J Stat Phys 122, 1215–1236 (2006). https://doi.org/10.1007/s10955-005-8023-9
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DOI: https://doi.org/10.1007/s10955-005-8023-9