Geodesic
Singular interaction potentials in classical statistical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 3, pp. 352-372 Cet article a éte moissonné depuis la source Math-Net.Ru

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A classical system of particles interacting through a stable two-body potential ts considered. It is shown that for a certain class of stable, essentially singular potentials and sufficiently large value of the cutoff parameter the stability property of the potential is preserved. It is shown that the thermodynamic potentials (pressure, free energy density) and the correlation functions are asymptotically independent of the continuation of the potential in the neighborhood of the singularity. 
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     title = {Singular interaction potentials in classical statistical mechanics},
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V. A. Zagrebnov; L. A. Pastur. Singular interaction potentials in classical statistical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 3, pp. 352-372. http://geodesic.mathdoc.fr/item/TMF_1978_36_3_a6/

[1] V. A. Zagrebnov, Ann. of Phys. (N. Y.), 102 (1976), 108 | DOI | MR

[2] V. A. Zagrebnov, Mezhdunarodnyi simpozium po izbrannym problemam statisticheskoi mekhaniki. Dubna, 19-22 aprelya 1977 g. (sbornik annotatsii), D17-10529, OIYaI, 1977

[3] D. Ryuel, Statisticheskaya mekhanika (strogie rezultaty), «Mir», 1971

[4] M. E. Fisher, Arch. Rat. Mech. Anal., 17 (1964), 377 | DOI | MR

[5] T. Kato, Teoriya vozmuschenii lineinykh operatorov, «Mir», 1972 | MR | Zbl

[6] M. Reed, B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-adjointness, Acad. Press, N. Y., 1975 | MR | Zbl

[7] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms, Princeton Univ. Press, New Jersey, 1971 | MR | Zbl

[8] H. Kalf, J. Walter, J. Functional Analysis, 10 (1972), 114 | DOI | MR | Zbl

[9] D. Ruelle, Commun. Math. Phys., 18 (1970), 127 | DOI | MR | Zbl

[10] R. L. Dobrushin, Teoriya veroyatn. i ee primen., 9 (1964), 626 | Zbl

[11] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, tom. I. Funktsionalnyi analiz, «Mir», 1977 ; А. Н. Колмогоров, С. В. Фомин, Элементы теорий функций и функционального анализа, «Наука», 1968 | MR | MR | Zbl

[12] E. Bekkenbakh, R. Bellman, Neravenstva, «Mir», 1965 | MR

[13] R. A. Minlos, A. Ya. Povzner, Tr. Mosk. matem. ob-va, 17 (1967), 243

[14] N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset, TMF, 1 (1969), 251