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Phase transition in one-dimensional nearest-neighbor systems. (English) Zbl 0333.60063


MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[1] Dobrushin, R. L., Description of a random field by means of conditional probabilities and the conditions governing its regularity, Theor. Probability Appl., 13, 197-224 (1968) · Zbl 0184.40403
[2] Doob, J. L.; Snell, J. L.; Williamson, R. E., Application of boundary theory to sums of independent random variables, (Hotelling Anniversary Volume (1960), Stanford University Press: Stanford University Press Stanford, Calif), 182-197 · Zbl 0094.32202
[3] Dynkin, E. B., The initial and final behavior of trajectories of Markov processes, Russian Math. Surveys (Uspekhi), 26, 165-182 (1971) · Zbl 0281.60087
[4] Dyson, F. J., Existence of a phase transition in a one dimensional Ising ferromagnet, Comm. Math. Phys., 12, 212-215 (1969) · Zbl 0172.01404
[5] H. FöllmerSém. Probabilité, Strasbourg; H. FöllmerSém. Probabilité, Strasbourg · Zbl 0367.60112
[6] Georgii, H.-O, Two remarks on extremal equilibrium states, Comm. Math. Phys., 32, 107-118 (1973)
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[8] Miyamoto, M., Martin-Dynkin boundaries of random fields, Comm. Math. Phys., 36, 321-324 (1974) · Zbl 0364.60116
[9] Preston, C. J., Gibbs States on Countable Sets (1974), Cambridge University Press: Cambridge University Press London/New York · Zbl 0297.60054
[10] Spitzer, F. L., Random fields and interacting particle systems, (Proc. M.A.A. Summer Seminar (1971), Math. Assoc. Amer: Math. Assoc. Amer Washington, DC) · Zbl 0124.34403
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