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Analyticity of the correlation functions for one-dimensional classical systems with power law decay of the potential
Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 13-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the one-dimensional Gibbs states for one-dimensional lattice and continuous systems where the interaction potential decays according to a power law. It is shown that for such systems the specific free energy and the correlation functions depend analytically on the potential. Bibliography: 18 titles. 
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R. L. Dobrushin. Analyticity of the correlation functions for one-dimensional classical systems with power law decay of the potential. Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 13-44. http://geodesic.mathdoc.fr/item/SM_1974_23_1_a1/

[1] R. L. Dobrushin, “Usloviya otsutstviya fazovykh perekhodov v odnomernykh klassicheskikh sistemakh”, Matem. sb., 93(135) (1974), 29–49 | Zbl

[2] D. Ryuel, Statisticheskaya mekhanika—strogie rezultaty, izd-vo «Mir», Moskva, 1971

[3] L. Van Hove, “Sur l'intégrale de configuration pour les systèmes de particules à une dimension”, Physica, 16:2 (1950), 137–143 | DOI | MR | Zbl

[4] H. Araki, “Gibbs states of a one dimensional quantum lattice”, Comm. Math. Phys., 14:2 (1969), 120–157 | DOI | MR | Zbl

[5] V. A. Statulyavichus, Issledovaniya po predelnym teoremam teorii veroyatnostei, Doktorskaya dissertatsiya, Vilnyus, 1957

[6] V. A. Statulyavichus, “O predelnykh teoremakh dlya sluchainykh funktsii, I”, Litov. matem. sb., 10:3 (1970), 583–592 | MR

[7] I. G. Zhurbenko, “Ob otsenke smeshannykh semivariantov dlya nekotorogo klassa sluchainykh protsessov”, Teoriya veroyatn., XV:3 (1970), 541–543 | MR | Zbl

[8] I. G. Zhurbenko, “O silnykh otsenkakh smeshannykh semivariantov sluchainykh protsessov”, Sib. matem. zh., 13:2 (1972), 293–308 | Zbl

[9] G. Gallavotti, T. F. Lin, “One dimensional lattice gases with rapidly decreasing interaction”, Arc. Rat. Mech. Anal., 37:3 (1970), 181–191 | DOI | MR

[10] R. L. Dobrushin, “Gibbsovskie sluchainye polya dlya reshetchatykh sistem s poparnym vzaimodeistviem”, Funkts. analiz, 2:4 (1968), 31–43 | MR

[11] R. L. Dobrushin, “Analiticity of correlation functions in one-dimensional classical systems with slowly decreasing potentials”, Comm. Math. Phys., 32:4 (1973), 269–289 | DOI | MR

[12] N. Danford, Dzh. Shvarts, Lineinye operatory. Obschaya teoriya, IL, Moskva, 1962

[13] R. Ganning, Kh. Rossi, Analiticheskie funktsii mnogikh kompleksnykh peremennykh, izd-vo «Mir», Moskva, 1969 | MR

[14] B. V. Shabat, Vvedenie v kompleksnyi analiz, izd-vo «Nauka», Moskva, 1969 | MR

[15] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, Moskva, 1962

[16] G. Gallavotti, S. Miracle-Sole, “A variational principle for the equilibrium of hard sphere system”, Ann. Inst. Henry Poincare, sec. A, 8:3 (1968), 287–299

[17] V. A. Statulyavichus, “Predelnye teoremy dlya summ sluchainykh velichin, svyazannykh v tsep Markova”, Litov. matem. sb., 9:2 (1969), 345–362; 3, 635–672; 10:1 (1970), 161–169

[18] V. A. Statuleviĉius, “On large deviations”, Z. Wahrsheinlichkeitstheorie, 6:2 (1965), 133–144 | DOI | MR