Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2016
- DOI:
- 10.48550/arXiv.1611.04547
- arXiv:
- arXiv:1611.04547
- Bibcode:
- 2016arXiv161104547J
- Keywords:
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- Mathematics - Dynamical Systems;
- 37A05;
- 37A60;
- 82B20;
- 82B26