WIAS Preprint No. 800, (2002)

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


  • Külske, Christof

2010 Mathematics Subject Classification

  • 82B44 82B26 82B20

2008 Physics and Astronomy Classification Scheme

  • 05.50.+q 61.43.-j 02.50.Cw


  • Disordered systems, non-Gibbsian measures, mean field models, Morita-approach, random field model, decimation transformation, diluted ferromagnet




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 properties of the conditional expectations 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. For a) we find 1) discontinuous dependence on the conditioning for almost any realization and 2) dependence of the conditional expectation 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 non-Gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean-field models.

Appeared in

  • J. Statist. Phys., 112 (2003), pp. 1079-1108. Electron. J.

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