Phase transitions in long-range Ising models and an optimal condition for factors of g-measures

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.

Öberg, Anders,1968-Uppsala universitet,Matematiska institutionen(Swepub:uu)aob27600 (author)
Pollicott, Mark,1959-University of Warwick (author)
Högskolan i GävleMatematiska institutionen (creator_code:org_t)

By the author/editor: Johansson, Ander ...; Öberg, Anders, 1 ...; Pollicott, Mark, ...

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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