Dobrushin, R. L. The problem of uniqueness of a Gibbsian random field and the problem of phase transitions. (English. Russian original) Zbl 0192.61702 Funct. Anal. Appl. 2, 302-312 (1968); translation from Funkts. Anal. Prilozh. 2, No. 4, 44-57 (1968). Reviewer: L. Arnold Page: −5 −4 −3 −2 −1 ±0 +1 Show Scanned Page Cited in 2 ReviewsCited in 107 Documents MSC: 82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics 82B26 Phase transitions (general) in equilibrium statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory Citations:Zbl 1183.82023 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] R. L. Dobrushin, ”Gibbsian random fields for lattice systems with paired interactions,” Funktsional’. Analiz i Ego Prilozhen.,2, No. 4, 31-43 (1968). [2] R. L. Dobrushin, ”Description of a random field by means of conditional probabilities and the conditions governing its regularity,” Teor. Veroyatn. i Ee Primen.,13, No. 2, 201-229 (1968). · Zbl 0184.40403 [3] R. A. Minlos, ”Regularity of the limiting Gibbsian distribution,” Funktsional’. Analiz i Ego Prilozhen.,1, No. 3, 40-53 (1967). [4] R. A. Minlos and Ya. G. Sinai, ”New results on phase transitions of the first kind in models of a lattice gas,” Trudy Mosk. Matem. Obshchestva,11, 213-242 (1967). [5] R. Griffiths, ”Peierl’s proof of spontaneous magnetization in two-dimensional Ising ferromagnet,” Phys. Rev.,A136, 437-438 (1964). [6] R. L. Dobrushin, ”Existence of a phase transition in the two-dimensional and three-dimensional Ising models,” Teor. Veroyatn. i Ee Primen.,10, No. 2, 209-230 (1965). · Zbl 0168.23803 [7] K. Huang, Statistical Mechanics, N. Y.-London, John Wiley (1963). [8] R. L. Dobrushin, Existence of Phase Transition in Models of a Lattice Gas, Proc. Fifth Berkeley Symp. on Math. Stat. and Probabilities, Vol. 3, Univ. of Calif. Press (1967), pp. 73-87. [9] D. Ruelle, Statistical Mechanics of a One-Dimensional Lattice Gas, Centre de Physique Theorique de l’Ecole Polytechnique, Preprint (1968). · Zbl 0165.29102 [10] R. E. Peierls, ”On Ising’s ferromagnet model,” Proc. Camb. Phil. Soc.,32, 477 (1936). · Zbl 0014.33604 · doi:10.1017/S0305004100019174 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.