2020/10/18 by Jean-René Chazottes, J. -R. Chazottes, Chazottes, J. -R. +3
Mathematics · Physics and Astronomy · #Atmospheric temperature range #Combinatorics #Dimension (graph theory) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Finite set #Geometry #Invariant (physics) #Inverse #Inverse temperature #Lattice (music) #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #Zero (linguistics) #Zero temperature #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.2010.08998
25 pages, 8 figures
openalex publication_date 2020/10/18 · arxiv created 2020/10/20 · arxiv updated 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct finite-range interactions on Sℤ2, where S is a finite set, for which the associated equilibrium states (i.e., the shift-invariant Gibbs states) fail to converge as temperature goes to zero. More precisely, if we pick any one-parameter family (μβ)β>0 in which μβ is an equilibrium state at inverse temperature β for this interaction, then limβ→∞μβ does not exist. This settles a question posed by the first author and Hochman who obtained such a non-convergence behavior when d≥ 3, d being the dimension of the lattice.