From PCA's to equilibrium systems and back

DOI10.1007/BF01217769zbMath0683.68045OpenAlexW2024281244MaRDI QIDQ1825034

Roelof Kuik, Joel L. Lebowitz, Sheldon Goldstein, Christian Maes

Publication date: 1989

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01217769

zbMATH Keywords

Gibbs statesprobabilistic cellular automata

Mathematics Subject Classification ID

Related Items (19)

Ergodicity of some classes of cellular automata subject to noise ⋮ Ergodicity of probabilistic cellular automata: A constructive criterion ⋮ Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible probabilistic cellular automata ⋮ Overview: PCA Models and Issues ⋮ Ising Model on the Torus and PCA Dynamics: Reversibility, Irreversibility, and Fast Tunneling ⋮ Nonequilibrium Physics Aspects of Probabilistic Cellular Automata ⋮ Partially ordered models ⋮ Sampling from a Gibbs measure with pair interaction by means of PCA ⋮ Probabilistic cellular automata with memory two: invariant laws and multidirectional reversibility ⋮ Equilibrium and non-equilibrium Ising models by means of PCA ⋮ Statistical mechanics of probabilistic cellular automata. ⋮ Probabilistic cellular automata and random fields with i.i.d. directions ⋮ Around probabilistic cellular automata ⋮ Probabilistic cellular automata for low-temperature 2-d Ising model ⋮ Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory ⋮ FKG inequalities in cellular automata and coupled map lattices ⋮ Parallel simulation of two-dimensional Ising models using probabilistic cellular automata ⋮ Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models ⋮ Large deviations and stationary measures for interacting particle systems

Cites Work

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• Some examples concerning the global Markov property
• Markov and stability properties of equilibrium states for nearest- neighbor interactions
• Remarks on the global Markov property
• Infinite systems with locally interacting components
• Gibbs measures and phase transitions
• Cellular automata and statistical mechanical models
• Statistical mechanics of probabilistic cellular automata.
• Commuting measure-preserving transformations
• Equivalence of Cellular Automata to Ising Models and Directed Percolation

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