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

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:

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
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
3. Corgini, M, “Gaussian domination in a quantum system of nonlinear oscillators”, Modern Physics Letters B, 13:12–13 (1999), 411
4. D. P. Sankovich, “Some Properties of Functional Integrals with Respect to the Bogoliubov Measure”, Theoret. and Math. Phys., 126:1 (2001), 121–135
5. M. Corgini, D. P. Sankovich, “Local Gaussian Dominance: An Anharmonic Excitation of Free Bosons”, Theoret. and Math. Phys., 132:1 (2002), 1019–1028
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
7. D. P. Sankovich, “The Bogolyubov Functional Integral”, Proc. Steklov Inst. Math., 251 (2005), 213–245
8. Sankovich D.P., “Gibbs Equilibrium Averages and Bogolyubov Measure”, Problems of Atomic Science and Technology, 2012, no. 1, 248–252
9. D. P. Sankovich, “Rigorous results of phase transition theory in lattice boson models”, Proc. Steklov Inst. Math., 290:1 (2015), 318–325
10. Sankovich D.P., “Proof of Bose Condensation For Weakly Interacting Lattice Bosons”, J. Phys. Commun., 2:10 (2018), UNSP 105015
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