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Two connections between random systems and non-Gibbsian measures

by Aernout C. D. van Enter , Christof Külske , 2008
"... ..."
Abstract - Cited by 8 (3 self) - Add to MetaCart
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3 Non-Gibbsianness for Majority-Rule Maps

by At High Fields, Aernout C. D. Van Enter, Roberto Fernández , 1994
"... We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian m ..."
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We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian

Introduction to (generalized) Gibbs measures

by Arnaud Le Ny
"... Abstract. In this monograph, we survey some key issues of the theory of Gibbsian and non-Gibbsian measures in finite-spin lattice systems. While ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
Abstract. In this monograph, we survey some key issues of the theory of Gibbsian and non-Gibbsian measures in finite-spin lattice systems. While

2003) Analogues of non-Gibbsianness in joint measures of disordered mean field models

by Christof Külske - J. Stat. Phys
"... It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity pro ..."
Abstract - Cited by 16 (7 self) - Add to MetaCart
It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity

Robustness of the non-Gibbsian property: some examples

by Aernout C. D. Van Enter, József Lorinczi - J. Phys. A , 1997
"... We discuss some examples of measures on lattice systems, which lack the property of being a Gibbs measure in a rather strong sense. 1 Introduction In recent years extensive research has been done on the occurrence of states (probability measures) on lattice systems which are not of Gibbsian type. ..."
Abstract - Cited by 24 (11 self) - Add to MetaCart
by Martinelli and Olivieri [36, 37], is to study how the non-Gibbsian measures behav...

Ecole Polytechnique Fédérale de Lausanne

by At High Fields, Aernout C. D. Van Enter , 2001
"... We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transi-tion temperature. We also show that majority transformations applied to the ..."
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We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transi-tion temperature. We also show that majority transformations applied to the

Instability of Renormalization-Group Pathologies under decimation

by F. Martinelli, E. Olivieri , 1995
"... We investigate the stability and instability of pathologies of renormalization group transformations for lattice spin systems under decimation. In particular we show that, even if the original renormalization group transformation gives rise to a non Gibbsian measure, Gibbsiannes may be restored by a ..."
Abstract - Cited by 15 (0 self) - Add to MetaCart
by applying an extra decimation trasformation. This fact is illustrated in details for the block spin transformation applied to the Ising model. We also discuss the case of another non-Gibbsian measure with nicely decaying correlations functions which remains non-Gibbsian after arbitrary decimation.

Gibbs vs. Non-Gibbs in the Equilibrium Ensemble Approach to Disordered Systems

by Related Fields, R. Kühn , 2004
"... Abstract. We describe the salient ideas of the equilibrium ensemble approach to disordered systems, paying due attention to the appearance of non-Gibbsian measures. A canonical scheme of approximations — constrained annealing — is described and characterised in terms of a Gibbs ’ variational princip ..."
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Abstract. We describe the salient ideas of the equilibrium ensemble approach to disordered systems, paying due attention to the appearance of non-Gibbsian measures. A canonical scheme of approximations — constrained annealing — is described and characterised in terms of a Gibbs ’ variational

Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

by At High Fields, Roberto Fernández, Aernout C. D. Van Enter, Rijksuniversiteit Groningen, Phb Ecublens , 1995
"... We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian m ..."
Abstract - Add to MetaCart
We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian

Gibbs vs. Non-Gibbs in the Equilibrium Ensemble Approach to Disordered Systems

by Reimer Kühn - Markov Proc. Relat. Fields , 2004
"... We describe the salient ideas of the equilibrium ensemble approach to disordered systems, paying due attention to the appearance of non-Gibbsian measures. A canonical scheme of approximations – constrained annealing – is described and characterised in terms of a Gibbs ’ variational principle for the ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
We describe the salient ideas of the equilibrium ensemble approach to disordered systems, paying due attention to the appearance of non-Gibbsian measures. A canonical scheme of approximations – constrained annealing – is described and characterised in terms of a Gibbs ’ variational principle
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