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Uspekhi Mat. Nauk, 1980, Volume 35, Issue 2(212), Pages 3–53 (Mi umn3192)  

This article is cited in 32 scientific papers (total in 32 papers)

Cluster expansions in lattice models of statistical physics and the quantum theory of fields

V. A. Malyshev


Full text: PDF file (2553 kB)
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English version:
Russian Mathematical Surveys, 1980, 35:2, 1–62

Bibliographic databases:

UDC: 519.2+519.9
MSC: 60G60, 60B05, 62H30, 82B20
Received: 16.03.1979

Citation: V. A. Malyshev, “Cluster expansions in lattice models of statistical physics and the quantum theory of fields”, Uspekhi Mat. Nauk, 35:2(212) (1980), 3–53; Russian Math. Surveys, 35:2 (1980), 1–62

Citation in format AMSBIB
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\by V.~A.~Malyshev
\paper Cluster expansions in lattice models of statistical physics and the quantum theory of fields
\jour Uspekhi Mat. Nauk
\yr 1980
\vol 35
\issue 2(212)
\pages 3--53
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571645}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1980RuMaS..35....1M}
\transl
\jour Russian Math. Surveys
\yr 1980
\vol 35
\issue 2
\pages 1--62
\crossref{https://doi.org/10.1070/RM1980v035n02ABEH001622}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. P. Virchenko, “Description of the phase with broken symmetry in the Ising model by the method of quasi-averages”, Theoret. and Math. Phys., 52:3 (1982), 927–938  mathnet  crossref  mathscinet  isi
    2. Yu. M. Sukhov, “Convergence to an equilibrium state for a one-dimensional quantum system of hard rods”, Math. USSR-Izv., 21:3 (1983), 547–583  mathnet  crossref  mathscinet  zmath
    3. I. A. Kashapov, “The spectrum of the transfer-matrix of fermion fields”, Russian Math. Surveys, 37:2 (1982), 213–214  mathnet  crossref  mathscinet  adsnasa  isi
    4. S. A. Molchanov, A. K. Stepanov, “Percolation in random fields. II”, Theoret. and Math. Phys., 55:3 (1983), 592–599  mathnet  crossref  mathscinet  isi
    5. D. E. Evans, J. T. Lewis, “The spectrum of the transfer matrix in theC*-algebra of the Ising model at high temperatures”, Comm Math Phys, 92:3 (1984), 309  crossref  mathscinet  zmath  adsnasa  isi
    6. Sh. S. Mamatov, “Bound states of the transfer matrix of the Ising model”, Theoret. and Math. Phys., 58:2 (1984), 140–143  mathnet  crossref  mathscinet  isi
    7. R. R. Akhmitzyanov, V. A. Malyshev, E. N. Petrova, “Cluster expansion for Gibbs perturbation of a massless Gaussian field”, Theoret. and Math. Phys., 58:2 (1984), 192–196  mathnet  crossref  mathscinet  isi
    8. I. V. Nikolaev, “Random cluster expansions in the high-temperature region”, Theoret. and Math. Phys., 60:3 (1984), 945–950  mathnet  crossref  mathscinet  isi
    9. R. A. Minlos, P. V. Khrapov, “Cluster properties and bound states of the Yang–Mills model with compact gauge group. I”, Theoret. and Math. Phys., 61:3 (1984), 1261–1265  mathnet  crossref  mathscinet  isi
    10. D. G. Martirosyan, “Uniqueness of Gibbs states in lattice models with one ground state”, Theoret. and Math. Phys., 63:2 (1985), 511–518  mathnet  crossref  mathscinet  isi
    11. A. G. Basuev, “Hamiltonian of the phase separation border and phase transitions of the first kind. I”, Theoret. and Math. Phys., 64:1 (1985), 716–734  mathnet  crossref  mathscinet  isi
    12. M. A. Shubin, “Pseudodifference operators and their Green's functions”, Math. USSR-Izv., 26:3 (1986), 605–622  mathnet  crossref  mathscinet  zmath
    13. S. A. Molchanov, A. K. Stepanov, “Percolation in random fields. III”, Theoret. and Math. Phys., 67:2 (1986), 434–439  mathnet  crossref  mathscinet  isi
    14. A. E. Mazel', “Phase diagram of the ANNNI model at low temperatures I. Rigorous results”, Theoret. and Math. Phys., 68:1 (1986), 722–730  mathnet  crossref  mathscinet  isi
    15. R. V. Bobrik, “Hierarchies of moment equations for the solution of the Schrödinger equation with random potential and their closure”, Theoret. and Math. Phys., 68:2 (1986), 841–847  mathnet  crossref  mathscinet  zmath  isi
    16. S. B. Shlosman, “Unusual analytic properties of some lattice models: Complement of Lee–Yang theory”, Theoret. and Math. Phys., 69:2 (1986), 1147–1150  mathnet  crossref  mathscinet  isi
    17. S. A. Pirogov, “Coexistence of phases in a multicomponent lattice liquid with complex thermodynamic parameters”, Theoret. and Math. Phys., 66:2 (1986), 218–221  mathnet  crossref  mathscinet  isi
    18. V. A. Arzumanian, B. S. Nakhapetian, S. K. Pogosyan, “Cluster properties of classical lattice spin systems with vacuum”, Theoret. and Math. Phys., 67:1 (1986), 331–339  mathnet  crossref  mathscinet  isi
    19. S. N. Isakov, “Phase diagrams and singularity at the point of a phase transition of the first kind in lattice gas models”, Theoret. and Math. Phys., 71:3 (1987), 638–648  mathnet  crossref  mathscinet  isi
    20. A. L. Rebenko, “Mathematical foundations of equilibrium classical statistical mechanics of charged particles”, Russian Math. Surveys, 43:3 (1988), 65–116  mathnet  crossref  mathscinet  adsnasa  isi
    21. A. E. Mazel', “Ising model on a face-centered cubic lattice at low temperatures”, Theoret. and Math. Phys., 74:1 (1988), 89–95  mathnet  crossref  mathscinet  isi
    22. Christian Borgs, Roger Waxler, “First order phase transitions in unbounded spin systemsI: Construction of the phase diagram”, Comm Math Phys, 126:2 (1989), 291  crossref  mathscinet  zmath  isi
    23. V. A. Malyshev, Ya. G. Sinai, “Some Research in Ergodic Theory and Mathematical Problems of Statistical Mechanics in the Moscow University Department of Probability Theory”, Theory Probab Appl, 34:1 (1989), 186  mathnet  crossref  mathscinet  zmath  isi
    24. Liudas Giraitis, Hira Koul, “Estimation of the dependence parameter in linear regression with long-range-dependent errors”, Stochastic Processes and their Applications, 71:2 (1997), 207  crossref
    25. Azer Kerimov, “The relationship between phase transitions and percolation in models with ground-state degeneracy”, J Phys A Math Gen, 35:26 (2002), 5365  crossref  mathscinet  zmath  isi  elib
    26. Mccullagh, P, “The permanental process”, Advances in Applied Probability, 38:4 (2006), 873  crossref  mathscinet  zmath  isi
    27. Roberto Fernández, Aldo Procacci, “Cluster Expansion for Abstract Polymer Models. New Bounds from an Old Approach”, Comm Math Phys, 274:1 (2007), 123  crossref  mathscinet  zmath  isi
    28. Assane Lo, “On the exponential decay of the n-point correlation functions and the analyticity of the pressure”, J Math Phys (N Y ), 48:12 (2007), 123506  crossref  mathscinet  zmath  isi  elib
    29. Suren Poghosyan, Daniel Ueltschi, “Abstract cluster expansion with applications to statistical mechanical systems”, J Math Phys (N Y ), 50:5 (2009), 053509  crossref  mathscinet  zmath  isi  elib
    30. Florin Avram, Nikolai Leonenko, Ludmila Sakhno, “On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields”, Probability and Statistics, 14 (2010), 210  crossref  elib
    31. Thiago Morais, Aldo Procacci, “Continuous Particles in the Canonical Ensemble as an Abstract Polymer Gas”, J Stat Phys, 2013  crossref
    32. Florin Avram, Nikolai Leonenko, Ludmila Sakhno, “Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities”, Stochastic Processes and their Applications, 2014  crossref
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