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TMF, 1989, Volume 79, Number 3, Pages 460–472 (Mi tmf4894)  

This article is cited in 10 scientific papers (total in 10 papers)

Gaussian dominance and phase transitions in systems with continuous symmetry

D. P. Sankovich


Abstract: Within the Fröhlich strategy of the phase transitions theory in systems with continuous symmetry, the existence of nonunique state in the nonideal Bose gas for sufficiently small temperatures is proved. We use the technique of majorizing estimates for the correlation expectations and the holomorphic representation of the functional integral method. The main role in the approach is played by the condition of the Gaussian domination by Fr̈ohlich–Simon–Spencer which we extend to the continuous case under consideration. Equation for the critical temperature and an upper bound for the energy of elementary excitations is derived.

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English version:
Theoretical and Mathematical Physics, 1989, 79:3, 656–665

Bibliographic databases:

Received: 15.02.1988

Citation: D. P. Sankovich, “Gaussian dominance and phase transitions in systems with continuous symmetry”, TMF, 79:3 (1989), 460–472; Theoret. and Math. Phys., 79:3 (1989), 656–665

Citation in format AMSBIB
\Bibitem{San89}
\by D.~P.~Sankovich
\paper Gaussian dominance and phase transitions in~systems with continuous symmetry
\jour TMF
\yr 1989
\vol 79
\issue 3
\pages 460--472
\mathnet{http://mi.mathnet.ru/tmf4894}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1015286}
\transl
\jour Theoret. and Math. Phys.
\yr 1989
\vol 79
\issue 3
\pages 656--665
\crossref{https://doi.org/10.1007/BF01016553}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989CJ64600014}


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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. N. N. Bogolyubov (Jr.), D. P. Sankovich, “N. N. Bogolyubov and statistical mechanics”, Russian Math. Surveys, 49:5 (1994), 19–49  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Corgini, M, “Rigorous estimates for correlation functions and existence of phase transitions in some models of interacting bosons”, International Journal of Modern Physics B, 11:28 (1997), 3329  crossref  isi
    3. Corgini, M, “Gaussian domination in a quantum system of nonlinear oscillators”, Modern Physics Letters B, 13:12–13 (1999), 411  crossref  isi
    4. D. P. Sankovich, “Some Properties of Functional Integrals with Respect to the Bogoliubov Measure”, Theoret. and Math. Phys., 126:1 (2001), 121–135  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. M. Corgini, D. P. Sankovich, “Local Gaussian Dominance: An Anharmonic Excitation of Free Bosons”, Theoret. and Math. Phys., 132:1 (2002), 1019–1028  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. Bernal, M. Corgini, D. P. Sankovich, “Nonideal Bose Gases: Correlation Inequalities and Bose Condensation”, Theoret. and Math. Phys., 139:3 (2004), 866–877  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. D. P. Sankovich, “The Bogolyubov Functional Integral”, Proc. Steklov Inst. Math., 251 (2005), 213–245  mathnet  mathscinet  zmath
    8. Sankovich D.P., “Gibbs Equilibrium Averages and Bogolyubov Measure”, Problems of Atomic Science and Technology, 2012, no. 1, 248–252  isi
    9. D. P. Sankovich, “Rigorous results of phase transition theory in lattice boson models”, Proc. Steklov Inst. Math., 290:1 (2015), 318–325  mathnet  crossref  crossref  isi  elib  elib
    10. Sankovich D.P., “Proof of Bose Condensation For Weakly Interacting Lattice Bosons”, J. Phys. Commun., 2:10 (2018), UNSP 105015  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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