Abstract:
We consider a wide class of one-dimensional systems in classical statistical physics which includes both continuous and lattice models. We prove a result concerning the uniqueness of the Gibbs state which generalizes earlier known results. As a consequence of this result we prove the differentiability of the free energy and the uniformly strong mixing property of Gibbs random processes.
Bibliography: 20 titles.
\Bibitem{Dob74}
\by R.~L.~Dobrushin
\paper Conditions for the absence of phase transitions in one-dimensional classical systems
\jour Math. USSR-Sb.
\yr 1974
\vol 22
\issue 1
\pages 28--48
\mathnet{http://mi.mathnet.ru/eng/sm2956}
\crossref{https://doi.org/10.1070/SM1974v022n01ABEH001684}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=386568}
\zmath{https://zbmath.org/?q=an:0307.60081}
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https://doi.org/10.1070/SM1974v022n01ABEH001684
https://www.mathnet.ru/eng/sm/v135/i1/p29
This publication is cited in the following 13 articles:
Manaka Okuyama, Masayuki Ohzeki, “Existence of Long-Range Order in Random-Field Ising Model on Dyson Hierarchical Lattice”, J Stat Phys, 192:2 (2025)
Marzio Cassandro, Enza Orlandi, Pierre Picco, “Typical Gibbs Configurations for the 1d Random Field Ising Model with Long Range Interaction”, Commun. Math. Phys., 309:1 (2012), 229
Gibbs Measures and Phase Transitions, 2011, 495
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Gibbs Measures and Phase Transitions, 1988
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L. A. Grigorenko, “Symmetric events for some stationary sequences”, Russian Math. Surveys, 39:1 (1984), 159–160
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Yu. M. Sukhov, “Steady solutions of the BBGKY hierarchy and first integrals of the motion of a system of classical particles One-dimensional case”, Theoret. and Math. Phys., 55:1 (1983), 365–372
K. M. Khanin, “Absence of phase transitions in one-dimensional long-range spin systems with random Hamiltonian”, Theoret. and Math. Phys., 43:2 (1980), 445–449
Sergio Albeverio, Raphael Høegh-Krohn, “Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions”, Comm Math Phys, 68:2 (1979), 95
S. B. Shlosman, “Absence of continuous symmetry breaking in two-dimensional models of statistical physics”, Theoret. and Math. Phys., 33:1 (1977), 897–902
R. L. Dobrushin, “Analyticity of the correlation functions for one-dimensional classical systems with power law decay of the potential”, Math. USSR-Sb., 23:1 (1974), 13–44
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