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Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Uppsala University.
University of Warwick.
2017 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417Article in journal (Refereed) Epub ahead of print
Abstract [en]

We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of -measures. Indag. Math. (N.S.) 22 (2011), 315–329] to a weaker condition, Berbee’s condition, in order for a one-block factor (a single-site renormalization) of the full shift space on finitely many symbols to have a -measure with a continuous -function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.

Place, publisher, year, edition, pages
2017.
National Category
Probability Theory and Statistics Mathematical Analysis
Identifiers
URN: urn:nbn:se:hig:diva-24122DOI: 10.1017/etds.2017.66OAI: oai:DiVA.org:hig-24122DiVA, id: diva2:1107562
Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2018-03-13Bibliographically approved

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Johansson, Anders

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