(Non-) Gibbsianness and phase transitions in random lattice spin models
| dc.creator | Kuelske, C. | |
| dc.date | 1999-04-26 | |
| dc.date.accessioned | 2026-07-07T04:32:47Z | |
| dc.date.available | 2026-07-07T04:32:47Z | |
| dc.description | We consider disordered lattice spin models with finite volume Gibbs measures $μ_Ł[η](d\s)$. Here $\s$ denotes a lattice spin-variable and $η$ a lattice random variable with product distribution $¶$ describing the disorder of the model. We ask: When will the joint measures $\lim_{Ł\uparrow\Z^d}¶(dη)μ_Ł[η](d\s)$ be [non-] Gibbsian measures on the product of spin-space and disorder-space? We obtain general criteria for both Gibbsianness and non-Gibbsianness providing an interesting link between phase transitions at a fixed random configuration and Gibbsianness in product space: Loosely speaking, a phase transition can lead to non-Gibbsianness, (only) if it can be observed on the spin-observable conjugate to the independent disorder variables. Our main specific example is the random field Ising model in any dimension for which we show almost sure- [almost sure non-] Gibbsianness for the single- [multi-] phase region. We also discuss models with disordered couplings, including spinglasses and ferromagnets, where various mechanisms are responsible for [non-] Gibbsianness. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/9904024 | |
| dc.identifier | http://arxiv.org/abs/math-ph/9904024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58325 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 82B44; 82B26; 82B20 | |
| dc.title | (Non-) Gibbsianness and phase transitions in random lattice spin models | |
| dc.type | text |