Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures
Dynamical Systems
2017-06-06 v2
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 -measure with a continuous -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.
Keywords
Cite
@article{arxiv.1611.04547,
title = {Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures},
author = {Anders Johansson and Anders Öberg and Mark Pollicott},
journal= {arXiv preprint arXiv:1611.04547},
year = {2017}
}