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Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
Univ Gavle, Dept Math, S-80176 Gavle, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England.
2019 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 39, p. 1317-1330Article in journal (Refereed) Published
Abstract [en]

We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of g-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 g-measure with a continuous g-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
2019. Vol. 39, p. 1317-1330
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-382245DOI: 10.1017/etds.2017.66ISI: 000462581800009OAI: oai:DiVA.org:uu-382245DiVA, id: diva2:1316038
Available from: 2019-05-15 Created: 2019-05-15 Last updated: 2019-05-15Bibliographically approved

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Öberg, Anders

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