caa a22 4500 467892482 CHVBK 20180406152753.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-005-8023-9 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8023-9 On the Truncation of Systems with Non-Summable Interactions [Elektronische Daten] [S. Friedli, B. de Lima] 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. Springer Science + Business Media, Inc., 2006 Long-range Potts model nationallicence percolation nationallicence phase transition nationallicence truncation nationallicence non-summable interaction nationallicence Friedli S. CBPF, Rua Dr. Xavier Sigaud 150, Urca CEP 22290-180, Rio de Janeiro, Brazil aut de Lima B. UFMG, Av. Antônio Carlos 6627, CEP 702 30123-970, Belo Horizonte, Brazil aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1215-1236 0022-4715 122:6<1215 2006 122 10955 https://doi.org/10.1007/s10955-005-8023-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8023-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Friedli S. CBPF, Rua Dr. Xavier Sigaud 150, Urca CEP 22290-180, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- de Lima B. UFMG, Av. Antônio Carlos 6627, CEP 702 30123-970, Belo Horizonte, Brazil aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1215-1236 0022-4715 122:6<1215 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer