Gibbs States on Countable Sets
From MaRDI portal
Publication:4051382
DOI10.1017/CBO9780511897122zbMath0297.60054MaRDI QIDQ4051382
Publication date: 1974
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Generalized stochastic processes (60G20) Stochastic processes (60G99) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)
Related Items
Asymptotics and spectral results for random walks on \(p\)-adics, Markov Chain Markov Field dynamics: Models and statistics, Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree, A random walk on \(p\)-adics -- the generator and its spectrum, Broadcasting on trees and the Ising model., Stochastic equilibria on graphs, I, Gibbs measures for fertile hard-core models on the Cayley tree, Occupation times for countable Markov chains. III: Chains on a tree with one branching point, Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree, Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree, Time-average for physical quantities in infinite classical systems, Weakly periodic Gibbs measures for HC-models on Cayley trees, Extremality of Gibbs measures for the \(HC\)-Blume-Capel model on the Cayley tree, Modelling and estimation of social interaction effects in new product diffusion, Limiting Gibbs measures of Potts model with countable set of spin values, Positive fixed points of quadratic operators and Gibbs measures, Random walks on lattices with points of two colors. II: Some rigorous inequalities for symmetric random walks, On ground states and phase transition for \(\lambda\)-model with the competing Potts interactions on Cayley trees, On an algebraic property of the disordered phase of the Ising model with competing interactions on a Cayley tree, Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree, State estimation for Cox processes on general spaces, Lower probabilities and function representation, Four competing interactions for models with an uncountable set of spin values on a Cayley tree, Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree, Phase transitions for a model with uncountable set of spin values on a Cayley tree, Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields, The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model, Applications of nonstandard analysis to spin models, Weakly periodic Gibbs measures in the HC-model for a normal divisor of index four, Boundary conditions and phase transitions in neural networks. Theoretical results, Gibbs measures for the three-state SOS model with external field on a Cayley tree, Periodic Gibbs measures and their extremes for the HC-Blume-Capel model in the case of a ``wand on the Cayley tree, The entropy of multiplicative subshifts on trees, Hidden Markov random fields and the genetic structure of the Scandinavian brown bear population, A new set of limiting Gibbs measures for the Ising model on a Cayley tree, Time asymptotics for some degenerate models of evolution of systems with an infinite number of particles, New weakly periodic Gibbs measures of Ising model on Cayley tree, On models with uncountable set of spin values on a Cayley tree: integral equations, The Potts model with countable set of spin values on a Cayley tree, Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees, A countable set of commuting self-adjoint operators and the algebra of local observables, On free energies of the Ising model on the Cayley tree, Extremity of the disordered phase in the Ising model on the Bethe lattice, Non-uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree, On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three, Translation-invariant extreme Gibbs measures for the Blume-Capel model withwand on a Cayley tree, Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model, Construction of a Markov field on an infinite tree, Phase transitions for models with a continuum set of spin values on a Bethe lattice, Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree, Localization of translation-invariant Gibbs measures for the Potts and ``solid-on-solid models on a Cayley tree, Statistical mechanics of probabilistic cellular automata., \(p\)-adic Gibbs measures and Markov random fields on countable graphs, Periodic Gibbs measures for the Potts model on the Cayley tree, Exact solution of a generalized ANNNI model on a Cayley tree, On weakly periodic Gibbs measures for the Potts model with external field on the Cayley tree, On quantum Markov chains on Cayley tree. III: Ising model, Mean-Field Bound on the 1-Arm Exponent for Ising Ferromagnets in High Dimensions, Quantum Markov states on Cayley trees, Entropy algebras and Birkhoff factorization, Gibbs measures and free energies of Ising–Vannimenus model on the Cayley tree, Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones, Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree, Translation-invariant Gibbs measures for fertile three-state ``hard core models on a Cayley tree, Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree, Markov random fields, Markov cocycles and the 3-colored chessboard, QUADRATIC STOCHASTIC OPERATORS AND PROCESSES: RESULTS AND OPEN PROBLEMS, Extremality of translation-invariant phases for a three-state SOS-model on the binary tree, Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree, Evolution algebras generated by Gibbs measures, The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree, Nonuniqueness of a Gibbs measure for the Ising ball model, A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree, The critical Ising model on trees, concave recursions and nonlinear capacity, Mixing time of critical Ising model on trees is polynomial in the height, Dynamic interaction models of economic equilibrium, Phase transition in one-dimensional nearest-neighbor systems, Ising models on the Lobachevsky plane, Periodic \(p\)-adic Gibbs measures of \(q\)-state Potts model on Cayley trees. I: The chaos implies the vastness of the set of \(p\)-adic Gibbs measures, Random time evolution of infinite particle systems, Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method, Periodic Gibbs measures for the Potts-SOS model on a Cayley tree, Translation invariance of the periodic Gibbs measures for the Potts model on the Cayley tree, Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order \(k=3\), Weakly periodic Gibbs measures for the Ising model on the Cayley tree of order \(k=2\), Ground states and phase transition of the \(\lambda\) model on the Cayley tree, ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO, On the constructive description of Gibbs measures for the Potts model on a Cayley tree, On Ising model with four competing interactions on Cayley tree, Periodic and weakly periodic ground states corresponding to subgroups of index three for the Ising model on Cayley tree, The Ising model and percolation on trees and tree-like graphs, Thermodynamic limit and central limit theorem for point random fields in non-ergodic case, Markov fields on branching planes, Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model, Description of periodic extreme Gibbs measures of some lattice models on the Cayley tree, Gibbs measures for the SOS model with four states on a Cayley tree, Order properties of attractive spin systems, Random economies with many interacting agents, Strict inequality for critical values of Potts models and random-cluster processes, Block Markov chains on trees, Coulomb and Riesz gases: The known and the unknown, Extremality of some Gibbs measures for the Blume–Capel HC-model on a Cayley tree, A HC model with countable set of spin values: Uncountable set of Gibbs measures, On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Asymptotic pressure on some self-similar trees, Generalisation of the Hammersley-Clifford theorem on bipartite graphs, Some non-periodic \(p\)-adic generalized Gibbs measures for the Ising model on a Cayley tree of order \(k\), Absolute continuity of non-homogeneous Gibbs measures of the Ising model on the Cayley tree, On $(k_0)$-translation-invariant and $(k_0)$-periodic Gibbs measures for Potts model on Cayley tree, Gibbs measures for HC-model with a cuountable set of spin values on a Cayley tree, Combinatorial statistics and the sciences, Using new approaches to obtain Gibbs measures of Vannimenus model on a Cayley tree, Periodic and weakly periodic ground states corresponding to the subgroups of index three for the Ising model on the Cayley tree of order three, On dynamical systems of quadratic stochastic operators constructed for bisexual populations, Gibbs periodic measures for a two-state HC-model on a Cayley tree, Potts model on a Cayley tree: a new class of Gibbs measures, Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree, Periodic ground states for the mixed spin Ising model with competing interactions on a Cayley tree, New class of Gibbs measures for two-state hard-core model on a Cayley tree, Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees, Canonical gibbs states, their relation to gibbs states, and applications to two-valued Markov chains, Unnamed Item, On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field, What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain‐of‐bundles model, A Three State Hard-Core Model on a Cayley Tree, A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree, The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice, Combinatorial criteria for uniqueness of Gibbs measures, Specific characteristics and variational principle for homogeneous random fields, Combinatorial applications of an inequality from statistical mechanics, GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS, QUANTUM MARKOV FIELDS ON GRAPHS, Fast mixing for independent sets, colorings, and other models on trees, An ?Inner? Variational Principle for Markov Fields on a Graph, On the relation between Markov random fields and social networks*, A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree, Champs markoviens et mesures de Gibbs sur ${R}$, On Non-Volterra Quadratic Stochastic Operators Generated by a Product Measure, Extremality of translation-invariant Gibbs measures for the Potts–SOS model on the Cayley tree, Ising model on the Cayley tree of second order with left and right interactions, Anisotropic Ising Model with Countable Set of Spin Values on Cayley Tree, Positive Fixed Points of Cubic Operators on R² and Gibbs Measures, A stochastic interactive model for the diffusion of information, Gibbs measures of Potts model on Cayley trees: A survey and applications, Phase transition and Gibbs measures of Vannimenus model on semi-infinite Cayley tree of order three
