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Uspekhi Mat. Nauk, 1968, Volume 23, Issue 1(139), Pages 133–190 (Mi umn5594)  

This article is cited in 21 scientific papers (total in 21 papers)

Lectures on statistical physics

R. A. Minlos

Abstract: These lectures contain a discussion of the fundamental concepts of statistical physics, such as the Gibbs distribution, correlation functions, magnitudes in thermodynamics, etc. Besides concepts that are familiar to physicists, the lectures introduce some new theorems and developments of a more mathematical character, namely, the limiting Gibbs distribution, van Hove's theorem, and equations for limiting correlation functions in lattice systems.
The lecture on phase transitions of the first kind is the hub of the article; it contains the greater part of the known mathematical results concerning phase transitions of the first kind in lattice systems.

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English version:
Russian Mathematical Surveys, 1968, 23:1, 137–196

Bibliographic databases:

UDC: 519.24
MSC: 62Exx, 62H20, 82B30, 82B20, 82B26, 00B05
Received: 11.09.1967

Citation: R. A. Minlos, “Lectures on statistical physics”, Uspekhi Mat. Nauk, 23:1(139) (1968), 133–190; Russian Math. Surveys, 23:1 (1968), 137–196

Citation in format AMSBIB
\by R.~A.~Minlos
\paper Lectures on statistical physics
\jour Uspekhi Mat. Nauk
\yr 1968
\vol 23
\issue 1(139)
\pages 133--190
\jour Russian Math. Surveys
\yr 1968
\vol 23
\issue 1
\pages 137--196

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    This publication is cited in the following articles:
    1. A. M. Khalfina, “The limiting equivalence of the canonical and grand canonical ensembles (low density case)”, Math. USSR-Sb., 9:1 (1969), 1–52  mathnet  crossref  mathscinet
    2. G. Gallavotti, “Boundary conditions and correlation functions in the ν-dimensional Ising model at low temperature”, Comm Math Phys, 23:4 (1971), 275  crossref  mathscinet  zmath  adsnasa
    3. I. L. Simyatitskii, “Comments on the paper “Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism” by N. N. Bogolyubov, D. Ya. Petrina, and B. I. Khatset”, Theoret. and Math. Phys., 6:2 (1971), 169–174  mathnet  crossref
    4. B. M. Gurevich, Ya. G. Sinai, Yu. M. Sukhov, “On invariant measures of dynamical systems of one-dimensional statistical mechanics”, Russian Math. Surveys, 28:5 (1973), 49–86  mathnet  crossref  mathscinet  zmath
    5. F. A. Berezin, “Some remarks on the wigner distribution”, Theoret. and Math. Phys., 17:3 (1973), 1163–1171  mathnet  crossref  mathscinet  zmath
    6. Sergio Albeverio, Raphael Høegh-Krohn, “Homogeneous random fields and statistical mechanics”, Journal of Functional Analysis, 19:3 (1975), 242  crossref
    7. Nguyen Xuan Xanh, Hans Zessin, “Punktprozesse mit Wechselwirkung”, Z Wahrscheinlichkeitstheorie verw Gebiete, 37:2 (1976), 91  crossref  mathscinet  zmath
    8. A. M. Dolotkazina, “Local limit theorem for a system of particles without hard core”, Theoret. and Math. Phys., 27:2 (1976), 439–442  mathnet  crossref  mathscinet
    9. R. L. Dobrushin, R. A. Minlos, “Polynomials in linear random functions”, Russian Math. Surveys, 32:2 (1977), 71–127  mathnet  crossref  mathscinet  zmath
    10. R. A. Minlos, S. K. Pogosyan, “Estimates of Ursell functions, group functions, and their derivatives”, Theoret. and Math. Phys., 31:2 (1977), 408–418  mathnet  crossref  mathscinet
    11. S. Albeverio, M. Ribeiro de Faria, R. Høegh-Krohn, “Stationary measures for the periodic Euler flow in two dimensions”, J Statist Phys, 20:6 (1979), 585  crossref  mathscinet  adsnasa
    12. Xuan Xanh Nguyen, Hans Zessin, “Ergodic theorems for spatial processes”, Z Wahrscheinlichkeitstheorie verw Gebiete, 48:2 (1979), 133  crossref  mathscinet  zmath
    13. M. Theodosopulu, A.P. Grecos, “On the derivation of linearized hydrodynamics from kinetic theory”, Physica A: Statistical Mechanics and its Applications, 95:1 (1979), 35  crossref
    14. G. I. Nazin, “Topological structure of the family of solutions of the Bogolyubov equation”, Theoret. and Math. Phys., 42:2 (1980), 159–166  mathnet  crossref  mathscinet  isi
    15. David Klein, “Dobrushin uniqueness techniques and the decay of correlations in continuum statistical mechanics”, Comm Math Phys, 86:2 (1982), 227  crossref  mathscinet  zmath  isi
    16. V. A. Zagrebnov, “A new proof and generalization of the Bogolyubov–Ruelle theorem”, Theoret. and Math. Phys., 51:3 (1982), 570–579  mathnet  crossref  mathscinet  isi
    17. Koji Kuroda, “Phase separations in Ising model with free boundary condition”, J Statist Phys, 30:1 (1983), 1  crossref  mathscinet  adsnasa  isi
    18. V. A. Zagrebnov, V. V. Papoyan, “The ensemble equivalence problem for Bose systems (nonideal Bose gas)”, Theoret. and Math. Phys., 69:3 (1986), 1240–1253  mathnet  crossref  mathscinet  isi
    19. David Klein, Wei-Shih Yang, “Absence of phase transitions for continuum models of dimension d>1”, J Math Phys (N Y ), 29:5 (1988), 1130  crossref  mathscinet  zmath  isi
    20. Krystyna Parczyk, Tomasz Masłowski, “Thermodynamic limit and central limit theorem for point random fields in non-ergodic case”, Reports on Mathematical Physics, 26:1 (1988), 1  crossref
    21. V. V. Ryazanov, “Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method”, Theoret. and Math. Phys., 194:3 (2018), 390–403  mathnet  crossref  crossref  isi  elib
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