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Robustness of the nonGibbsian property: some examples
 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. ..."
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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. Such measures occur for example in renormalizationgroup studies [17, 18, 21, 8, 9, 10, 11, 12, 13, 40], nonequilibrium statistical mechanical models [42, 26, 33, 38], image analysis [5, 15, 34], probabilistic cellular automata [25, 33] and random cluster models [19, 39]. The possibility of their occurrence and their properties have been considered by various authors [1, 7, 14, 20, 22, 24, 28, 29, 30, 31, 32, 36, 37, 41, 44]. This nonGibbsian behaviour has often been considered `pathological'  undesirable , and there have been various attempts to control the nonGibbsianness. One approach, advocated by Martinelli and Olivieri [36, 37], is to study how the nonGibbsian measures behav...
On the possible failure of the Gibbs property for measures on lattice systems.
 Markov Proc. Rel. Fields
, 1996
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Illdefined blockspin transformations at arbitrarily high temperatures,
 J. Stat. Phys.
, 1996
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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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Renormalization Group, NonGibbsian states, their relationship and further developments
, 2005
"... We review what we have learned about the “Renormalization Group peculiarities ” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the ..."
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We review what we have learned about the “Renormalization Group peculiarities ” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the study of nonGibbsian states (probability measures). We also mention some further related developments, which find applications in nonequilibrium questions and disordered models.
Pathological Behavior of RenormalizationGroup Maps at High Fields and Above the Transition Temperature
, 1995
"... We show that decimation transformations applied to highq Potts models result in nonGibbsian 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 nonGibbsian m ..."
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We show that decimation transformations applied to highq Potts models result in nonGibbsian 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 nonGibbsian measures. This shows that pathological behavior of renormalizationgroup transformations is even more widespread than previous examples already suggested. Contents 1 Introduction 1 2 Basic Setup 2 3 NonGibbsianness for MajorityRule Maps of Ising Models at High Magnetic Field 4 3.1 Proof of Claim 3.2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 3.2 Proof of Claim 3.3 : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 4 NonGibbsianness of Decimated Potts Models Above the Transition Temperature 15 4.1 Lack of Complete Analyticity Above T c : : : : : : : : : : : : : : : : : 15 4.2 NonGibbsianness for a Sequence of Temperatures Above T c : : : : : : : : : : : : : : :...
3 NonGibbsianness for MajorityRule Maps
, 1994
"... We show that decimation transformations applied to highq Potts models result in nonGibbsian 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 nonGibbsian m ..."
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We show that decimation transformations applied to highq Potts models result in nonGibbsian 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 nonGibbsian measures. This shows that pathological behavior of renormalizationgroup transformations is even more widespread than previous examples already suggested.
Ecole Polytechnique Fédérale de Lausanne
, 2001
"... We show that decimation transformations applied to highq Potts models result in nonGibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the ..."
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We show that decimation transformations applied to highq Potts models result in nonGibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the