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Ergodicity ofL2-Semigroups and Extremality of Gibbs States by Sergio Albeverio; Yuri G. Kondratiev; Michael Röckner is a Mathematics article available to read on EtoBox.

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dedicated to our admired colleague and friend professor masatoshi fukushima on the occasion of his 60th birthday We extend the classical results of Holley Stroock on the characterization of extreme Gibbs states for the Ising model in terms of the irreducibility (resp. ergodicity) of the corresponding Glauber dynamics to the case of lattice systems with unbounded (linear) spin spaces. We first develop a general framework to discuss questions of this type using classical Dirichlet forms on infinite dimensional state spaces and their associated diffusions. We then describe concrete applications to lattice models with polynomial interactions (i.e., the discrete P(.) d -models of Euclidean quantum field theory). In addition, we prove the equivalence of extremality and shiftergodicity for tempered Gibbs states of these models and also discuss this question in the general framework. 1997 Academic Press ## 1. INTRODUCTION AND PRELIMINARIES Since the classical work of Holley and Stroock (cf. [HSt76]) it is wellknown that in the Ising model a Gibbs state + is extremal if and only if the semigroup of operators given by the corresponding Glauber dynamics considered as an L 2 (+)-semigroup is i

Who reads Ergodicity ofL2-Semigroups and Extremality of Gibbs States?

Author

Sergio Albeverio; Yuri G. Kondratiev; Michael Röckner

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)