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• W2015651405 abstract "We consider a class of discrete $q$-state spin models defined in terms of a translation-invariant quasilocal specification with discrete clock-rotation invariance which have extremal Gibbs measures $mu'_{varphi }$ labeled by the uncountably many values of $varphi $ in the one-dimensional sphere (introduced by van Enter, Opoku, Külske [J. Phys. A 44 (2011) 475002, 11]). In the present paper we construct an associated Markov jump process with quasilocal rates whose semigroup $(S_{t})_{tgeq0}$ acts by a continuous rotation $S_{t}(mu'_{varphi })=mu'_{varphi +t}$. As a consequence our construction provides examples of interacting particle systems with unique translation-invariant invariant measure, which is not long-time limit of all starting measures, answering an old question (compare Liggett [Interacting Particle Systems (1985) Springer], question four, Chapter one). The construction of this particle system is inspired by recent conjectures of Maes and Shlosman about the intermediate temperature regime of the nearest-neighbor clock model. We define our generator of the interacting particle system as a (noncommuting) sum of the rotation part and a Glauber part. Technically the paper rests on the control of the spread of weak nonlocalities and relative entropy-methods, both in equilibrium and dynamically, based on Dobrushin-uniqueness bounds for conditional measures." @default.
• W2015651405 created "2016-06-24" @default.
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• W2015651405 date "2014-12-01" @default.
• W2015651405 modified "2023-09-27" @default.
• W2015651405 title "A class of nonergodic interacting particle systems with unique invariant measure" @default.
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• W2015651405 doi "https://doi.org/10.1214/13-aap987" @default.
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