Rigorous analysis of discontinuous phase transitions via mean-field bounds
| dc.creator | Biskup, Marek | |
| dc.creator | Chayes, Lincoln | |
| dc.date | 2002-07-25 | |
| dc.date | 2003-09-30 | |
| dc.date.accessioned | 2026-07-07T04:49:51Z | |
| dc.date.available | 2026-07-07T04:49:51Z | |
| dc.description | We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z^d. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean-field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on Z^d undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q>=3, the r-component cubic models with r>=4 and the O(N)-nematic liquid-crystal models with N>=3. | |
| dc.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207242 | |
| dc.identifier | http://arxiv.org/abs/math/0207242 | |
| dc.identifier | Commun. Math. Phys. 238 (2003), no. 1-2, 53-93 | |
| dc.identifier | doi:10.1007/s00220-003-0828-2 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64587 | |
| dc.subject | Probability | |
| dc.subject | 82B05; 82B26; 82B20 | |
| dc.title | Rigorous analysis of discontinuous phase transitions via mean-field bounds | |
| dc.type | text |