Metastates in disordered mean-field models: Random field and hopfield models
Copyright policy )Metastates in disordered mean-field models: Random field and hopfield models
We rigorously investigate the size dependence of disordered mean field models with finite local spin space in terms of metastates. Thereby we provide an illustration of the framework of metastates for systems of randomly competing Gibbs measures. In particular we consider the thermodynamic limit of the empirical metastate 1/N ∑<sup>N</sup><sub>n=1</sub> δμ<sub>n</sub>(η) where μ<sub>n</sub>(η) is the Gibbs measure in the finite volume {1,...,n} and the frozen disorder variable η is fixed. We treat explicitely the Hopfield model with finitely many patterns and the Curie Weiss Random Field Ising model. In both examples in the phase transition regime the empirical metastate is dispersed for large N. Moreover it does not converge for a.e. η but rather in distribution for whose limits we give explicit expressions. We also discuss another notion of metastates, due to Aizenman and Wehr.
- University of Groningen Netherlands
- Leibniz Association Germany
- Weierstrass Institute Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
Random Gibbs States, metastates, 82B44, size dependence, Mean Field Models, ISING-MODEL, 530, 510, Random Field Model, Hopfield Model, mean-field models, SYSTEMS, Metastates, disordered systems, Disordered Systems, 60K40, GIBBS-STATES, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, ddc:510, random Gibbs measures, Disordered Systems -- Size Dependence -- Random Gibbs States -- Metastates -- Mean Field Models -- Hopfield Model -- Random Field Model, Size Dependence, ddc:530, article, random Gibbs states, mean field models, Hopfield model, 60G57, disordered system, random field model, Other physical applications of random processes, Random measures
Random Gibbs States, metastates, 82B44, size dependence, Mean Field Models, ISING-MODEL, 530, 510, Random Field Model, Hopfield Model, mean-field models, SYSTEMS, Metastates, disordered systems, Disordered Systems, 60K40, GIBBS-STATES, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, ddc:510, random Gibbs measures, Disordered Systems -- Size Dependence -- Random Gibbs States -- Metastates -- Mean Field Models -- Hopfield Model -- Random Field Model, Size Dependence, ddc:530, article, random Gibbs states, mean field models, Hopfield model, 60G57, disordered system, random field model, Other physical applications of random processes, Random measures
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).24 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!