Mean-field driven first-order phase transitions in systems with long-range interactions
| dc.creator | Biskup, Marek | |
| dc.creator | Chayes, Lincoln | |
| dc.creator | Crawford, Nicholas | |
| dc.date | 2005-01-27 | |
| dc.date | 2006-04-13 | |
| dc.date.accessioned | 2026-07-07T06:38:35Z | |
| dc.date.available | 2026-07-07T06:38:35Z | |
| dc.description | We consider a class of spin systems on $\Z^d$ with vector valued spins $(\bS_x)$ that interact via the pair-potentials $J_{x,y} \bS_x\cdot\bS_y$. 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 $d\ge3$, 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. | |
| dc.description | 57 pages; uses a (modified) jstatphys class file | |
| dc.identifier | https://arxiv.org/abs/math-ph/0501067 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0501067 | |
| dc.identifier | J. Statist. Phys. 122 (2006), no. 6, 1139-1193 | |
| dc.identifier | doi:10.1007/s10955-005-8072-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100786 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Probability | |
| dc.subject | 82B26; 82B05 | |
| dc.title | Mean-field driven first-order phase transitions in systems with long-range interactions | |
| dc.type | text |