(Non-) Gibbsianness and phase transitions in random lattice spin models

dc.creatorKuelske, C.
dc.date1999-04-26
dc.date.accessioned2026-07-07T04:32:47Z
dc.date.available2026-07-07T04:32:47Z
dc.descriptionWe 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.description24 pages
dc.identifierhttps://arxiv.org/abs/math-ph/9904024
dc.identifierhttp://arxiv.org/abs/math-ph/9904024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58325
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject82B44; 82B26; 82B20
dc.title(Non-) Gibbsianness and phase transitions in random lattice spin models
dc.typetext

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