caa a22 4500 467892474 CHVBK 20180406152753.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-005-8072-0 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8072-0 Mean-Field Driven First-Order Phase Transitions in Systems with Long-Range Interactions [Elektronische Daten] [Marek Biskup, Lincoln Chayes, Nicholas Crawford] We consider a class of spin systems on ℤ d with vector valued spins (S x ) that interact via the pair-potentials J x,y S x ⋅S y . The interactions are generally spread-out in the sense that the J x,y 's exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions d≥3, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions d = 1,2 for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique "state,” then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure. Springer Science + Business Media, Inc., 2006 First-order phase transitions nationallicence mean-field theory nationallicence infrared bounds nationallicence reflection positivity nationallicence mean-field bounds nationallicence Potts model nationallicence Blume-Capel model nationallicence Biskup Marek Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA aut Chayes Lincoln Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA aut Crawford Nicholas Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1139-1193 0022-4715 122:6<1139 2006 122 10955 https://doi.org/10.1007/s10955-005-8072-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8072-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Biskup Marek Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA aut NATIONALLICENCE 700 1- Chayes Lincoln Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA aut NATIONALLICENCE 700 1- Crawford Nicholas Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1139-1193 0022-4715 122:6<1139 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer