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Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
Högskolan i Gävle.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
University of Warwick.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We weaken the assumption of summable variations in a paper by Verbitskiy \cite{verb} to a weaker condition, Berbee's condition, in order for a 1-block factor (a single site renormalisation) 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 an inverse critical temperature in a one-sided long-range Ising model which is at most 8 times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.

National Category
Mathematical Analysis
Research subject
Mathematics
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URN: urn:nbn:se:uu:diva-319953OAI: oai:DiVA.org:uu-319953DiVA, id: diva2:1088164
Available from: 2017-04-11 Created: 2017-04-11 Last updated: 2017-04-12Bibliographically approved

Open Access in DiVA

fulltext 2016(272 kB)36 downloads
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File name FULLTEXT01.pdfFile size 272 kBChecksum SHA-512
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https://arxiv.org/abs/1611.04547

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CiteExportLink to record
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  • nn-NB
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  • Other locale
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Output format
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