2016/11/14 by Anders Johansson, Johansson, Anders, Anders Öberg +3 · 2 citations
Mathematics · Physics and Astronomy · #37A05 #37A60 #82B20 #82B26 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.DS #msc:37A05 #msc:37A60 #msc:82B20 #msc:82B26
paper · pdf · doi:10.48550/arxiv.1611.04547
openalex publication_date 2016/11/14 · arxiv created 2017/06/05 · arxiv updated 2017/06/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We weaken the assumption of summable variations in a paper by Verbitskiy \citeverb 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.