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arXiv · 1611.04547

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

Anders Johansson·Anders Öberg·Mark Pollicott
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Abstract

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.

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Anders Johansson, Anders Öberg, Mark Pollicott. 2016-11-14. Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures. https://arxiv.org/abs/1611.04547

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