Abstract:
A general investigation is made of the spherical model for arbitrary dispersion of
the volume integrals and lattice symmetry. It is shown that in this case a phase
transition takes place to a structure that in general is not commensurate with the
crystal lattice and is not destroyed by a magnetic field. The spontaneous and
longitudinal magnetic moments and critical temperature are found as functions of
the magnetic field. In addition, the physical meaning of the “sticking” of the saddle
point is clarified. With a view to establishing the part played by fluctuations, the
spherical model is considered for magnets with long but finite interaction range.
In this model, the temperature and magnetic field regions in which fluctuation effects
are important are determined, and it is shown that outside these regions the critical
exponents are equal to the exponents found in mean field theory. A magnet with two
inequivalent magnetic sublattices is investigated. It is shown that, depending on the
radii of the exchange integrals, phases that are anomalous from the point of view of
mean field theory can arise in such a system in the critical region.
Citation:
Yu. M. Ivanchenko, A. A. Lisyanskii, A. E. Filippov, “Fluctuation effects in the spherical model”, TMF, 66:2 (1986), 278–289; Theoret. and Math. Phys., 66:2 (1986), 183–190
\Bibitem{IvaLisFil86}
\by Yu.~M.~Ivanchenko, A.~A.~Lisyanskii, A.~E.~Filippov
\paper Fluctuation effects in the spherical model
\jour TMF
\yr 1986
\vol 66
\issue 2
\pages 278--289
\mathnet{http://mi.mathnet.ru/tmf4623}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=838281}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 66
\issue 2
\pages 183--190
\crossref{https://doi.org/10.1007/BF01017771}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986E417400012}
Linking options:
https://www.mathnet.ru/eng/tmf4623
https://www.mathnet.ru/eng/tmf/v66/i2/p278
This publication is cited in the following 2 articles:
V. L. Sobolev, I. M. Vitebsky, A. A. Lisyansky, “Magnetic phase transitions with final ordering: Peculiarities in the critical behavior”, Phys. Rev. B, 47:14 (1993), 8653
V.L. Sobolev, I.M. Vitebsky, A.A. Lisyansky, “Critical phenomena near the final ordering phase transition point in double magnetic systems”, Physics Letters A, 175:6 (1993), 450
Citation in format AMSBIB
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