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24
The Restriction of the Ising Model to a Layer
, 1998
"... We discuss the status of recent Gibbsian descriptions of the restriction (projection) of the Ising phases to a layer. We concentrate on the projection of the twodimensional low temperature Ising phases for which we prove a variational principle. ..."
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Cited by 8 (7 self)
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We discuss the status of recent Gibbsian descriptions of the restriction (projection) of the Ising phases to a layer. We concentrate on the projection of the twodimensional low temperature Ising phases for which we prove a variational principle.
Transformations of Gibbs measures
, 1998
"... We study local transformations of Gibbs measures. We establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies. General results are illustrated by simple examples. ..."
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Cited by 1 (0 self)
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We study local transformations of Gibbs measures. We establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies. General results are illustrated by simple examples.
Almost) Gibbsian description of the sign fields of SOS fields
"... An example is presented of a measure on a lattice system which has a measure zero set of points (configurations) where some conditional probability can be discontinuous, but does not become a Gibbs measure under decimation (or other) transformations. We also discuss some related issues. ..."
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An example is presented of a measure on a lattice system which has a measure zero set of points (configurations) where some conditional probability can be discontinuous, but does not become a Gibbs measure under decimation (or other) transformations. We also discuss some related issues.
[1] NonGibbsianness of the invariant measures of nonreversible cellular automata with totally asymmetric noise
, 2001
"... We present a class of random cellular automata with multiple invariant measures which are all d nonGibbsian. The automata have configuration space {0,1} Z, with d> 1, and they are noisy versions of automata with the “eroder property”. The noise is totally asymmetric in the sense that it allows r ..."
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We present a class of random cellular automata with multiple invariant measures which are all d nonGibbsian. The automata have configuration space {0,1} Z, with d> 1, and they are noisy versions of automata with the “eroder property”. The noise is totally asymmetric in the sense that it allows random flippings of “0 ” into “1 ” but not the converse. We prove that all invariant measures assign to the event “a sphere with a large radius L is filled with ones ” a probability µL that is too large for the measure to be Gibbsian. For example, for the NEC automaton ( − ln µL) ≍ L while for any Gibbs measure the corresponding value is ≍ L2. Key words: Gibbs vs. nonGibbs measures, cellular automata, invariant measures, nonergodicity, eroders, convex sets.
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.