On the absence of phase transition in continuous one-dimensional Gibbs systems with no hard core

✍ Scribed by F. Papangelou

• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 521 KB
• Volume: 74
• Category: Article
• ISSN: 1432-2064
• DOI: 10.1007/bf00363511

✦ Synopsis

It has been known for some time that one-dimensional continuous Gibbs systems specified by long range hard core pair potentials exhibit no phase transition, i.e. are uniquely determined by the potential, provided the tail of the potential has a finite first moment. The present paper deals with long range potentials which have no hard core but diverge appropriately at zero, and proves that they admit unique "regular" Gibbs systems at arbitrary temperature and activity level. Regularity here means that the expected numbers of particles in intervals of equal length are uniformly bounded.