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24
Almost Gibbsian versus weakly Gibbsian measures
 STOCH. PROC. APPL
, 1999
"... We consider two possible extensions of the standard de nition of Gibbs measures for lattice spin systems. When a random eld has conditional distributions which are almost surely continuous (almost Gibbsian eld), then there is a potential for that eld which is almost surely summable (weakly Gibbsian ..."
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Cited by 37 (13 self)
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We consider two possible extensions of the standard de nition of Gibbs measures for lattice spin systems. When a random eld has conditional distributions which are almost surely continuous (almost Gibbsian eld), then there is a potential for that eld which is almost surely summable (weakly Gibbsian eld). This generalizes the standard Kozlov theorems. The converse is not true in general as is illustrated by counterexamples.
Renormalization Group Pathologies and the Definition of Gibbs States
, 1998
"... We show that the socalled Renormalization Group pathologies in low temperature Ising models are due to the fact that the renormalized Hamiltonian is defined only almost everywhere (with respect to the renormalized Gibbs measures). We construct this renormalized Hamiltonian using a Renormalization G ..."
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Cited by 33 (0 self)
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We show that the socalled Renormalization Group pathologies in low temperature Ising models are due to the fact that the renormalized Hamiltonian is defined only almost everywhere (with respect to the renormalized Gibbs measures). We construct this renormalized Hamiltonian using a Renormalization Group method developed for random systems and we show that the pathologies are analogous to Griffiths' singularities.
Propagation of Gibbsianness for infinitedimensional Brownian diffusions, in preparation
"... We study the (strong)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion, when the initial distribution is Gibbsian. ..."
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Cited by 24 (2 self)
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We study the (strong)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion, when the initial distribution is Gibbsian.
On the possible failure of the Gibbs property for measures on lattice systems.
 Markov Proc. Rel. Fields
, 1996
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2003) Analogues of nonGibbsianness in joint measures of disordered mean field models
 J. Stat. Phys
"... It is known that the joint measures on the product of spinspace and disorder space are very often nonGibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this nonGibbsianness in the corresponding meanfield models? We study the continuity pro ..."
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Cited by 16 (7 self)
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It is known that the joint measures on the product of spinspace and disorder space are very often nonGibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this nonGibbsianness in the corresponding meanfield models? We study the continuity properties of the conditional probabilities in finite volume of the following mean field models: (a) joint measures of random field Ising, (b) joint measures of dilute Ising, (c) decimation of ferromagnetic Ising. The conditional probabilities are functions of the empirical mean of the conditionings; so we look at the large volume behavior of these functions to discover nontrivial limiting objects. For (a) we find (1) discontinuous dependence for almost any realization and (2) dependence of the conditional probabilities on the phase. In contrast to that we see continuous behavior for (b) and (c), for almost any realization. This is in complete analogy to the behavior of the corresponding lattice models in high dimensions. It shows that nonGibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of meanfield models. KEY WORDS: Disordered systems; nonGibbsian measures; mean field models; Moritaapproach; random field model; decimation transformation; diluted ferromagnet. 1.
Gibbs properties of the fuzzy Potts model on trees and in mean field
, 2008
"... We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which nonGibbsianness happens is given. The results for trees are somewhat less explicit, but we do ..."
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Cited by 13 (2 self)
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We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which nonGibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that nonGibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures. 1
Variational Principle for Some Renormalized Measures
, 1998
"... We show that some measures suffering from the socalled Renormalization Group pathologies satisfy a variational principle and that the corresponding limit of the pressure, with boundary conditions in a set of measure 1, is proportional to the pressure of the Ising model. ..."
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Cited by 11 (1 self)
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We show that some measures suffering from the socalled Renormalization Group pathologies satisfy a variational principle and that the corresponding limit of the pressure, with boundary conditions in a set of measure 1, is proportional to the pressure of the Ising model.
The renormalizationgroup peculiarities of Griffiths and Pearce: What have we learned?,
 in Mathematical Results in Statistical Mechanics (Proceedings of the colloquium with the same name, MarseilleLuminy,
, 1998
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