References
Dobrushin, R. L.: Description of a random field by means of conditional probabilities and regularity conditions. Probability theory and applications (in Russian)13 (2) 201–222 (1968).
Dobrushin, R. L.: Problem of uniqueness of a Gibbs random field and phase transitions. Functional Analysis and applications (in Russian)2 (4) 44–57 (1968).
Dobrushin, R. L.: Gibbs field: the general case. Functional analysis and applications (in Russian)3 (1) 27–35 (1969).
Ruelle, D.: Statistical mechanics of one-dimensional lattice gas, Commun. math. Phys.,9, (4) 267–278 (1968).
Ibragimov, I. A., Linnik, J. V.: Independent and stationnary dependent variables (In Russian) Science edit. 1965.
Dyson, F. J.: Existence of a phase transitions in one-dimensional Ising Ferromagnet,Commun. math. Phys.,12, (1) 91–107 (1969).
Fisher, M. E., Felderhof, B. U.: Phase transition in one-dimensional cluster-interaction fluids, IA, IB, II, III, Ann. Phys.,58, (1) 176–300 (1970).
Gallavotti, G., Miracle-Sole, S., Ruelle, D.: Absence of phase transition in one-dimensional systems with hard core, Phys. Lett.,A26, (8) 350–351 (1970).
Gallavotti, G., Miracle-Sole, S.: Absence of phase transitions in hard-core one-dimensional systems with long-range interactions, Journ. of Math. Phys.,11, (1) 147–154 (1969).
Ruelle, D.: Statistical mechanics-rigorous results, N.Y.-Amsterdam: W. A. Benjamin Inc., 1969.
Van Hove, L.: Sur l'intégrale de configuration pour les systèmes de particules à une dimension, Physica,16, 137–143 (1950).
Araki, H.: Gibbs states of one dimensional quantum lattice, Commun. math. Phys.,14, (2) 120–157, 1969.
Statuliavičus, V. A.: On limit theorems for stochastic functions I. Lithuanian Mathematical Collection (in Russian)10, (3) 583–592 (1970).
Žurbenko, I. G.: On the determination of mixed semi-invariants for some classes of random processes (in Russian) Theor. Prob. Appl.15 (3), 541–544 (1970).
Gallavotti, G.: Lin, T. F.: One dimensional lattice gases with rapidly decreasing interaction, Archive for Ration. Mech. and Analys.,37, (3) 181–191 (1970).
Feller, W.: An introduction to Probability Theory and its applications, vol. 1, New York: Wiley & Sons Inc., 1950.
Dobrushin, R. L.: Gibbs random fields for lattice systems with pair interactions. Functional analysis and applications (in Russian)2 (4) 31–43 (1968).
Lanford, O. E., Ruelle, D.: Observables at infinity and states with short-range correlations in statistical mechanics, Commun. math. Phys.,13, (3) 194–215 (1968).
Dunford, N., Schwartz, T.: Linear operators, Part 1, General Theory, New York-London: Interscience Publishers, 1958.
Gunning, R. G., Rossi, H.: Analytic functions of several complex variables, New York: Prentice Hall, 1965.
Shabat, B. V.: Introduction to complex analysis (in Russian) Science edit. 1669.
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Dobrushin, R.L. Analyticity of correlation functions in one-dimensional classical systems with slowly decreasing potentials. Commun.Math. Phys. 32, 269–289 (1973). https://doi.org/10.1007/BF01645609
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DOI: https://doi.org/10.1007/BF01645609