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No Longer Transcendental Equations in the Homogeneous Mean‐Field Theory of Ferromagnets
Author(s) -
Millev Y.,
Fähnle M.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221710221
Subject(s) - transcendental equation , mathematics , transcendental function , polynomial , ferromagnetism , brillouin and langevin functions , homogeneous , homogeneous polynomial , brillouin zone , transcendental number , mathematical analysis , degree (music) , field (mathematics) , function (biology) , magnetization , magnetic field , mathematical physics , physics , condensed matter physics , differential equation , quantum mechanics , pure mathematics , matrix polynomial , combinatorics , acoustics , evolutionary biology , biology
The transcendental equation for the determination of the magnetization within the mean‐field approximation is reduced to the problem of solving an explicit polynomial equation of degree 2 S where S is the spin of the localized magnetic moments. Various possibilities to achieve this reduction are pointed out and the physically most tractable variant is singled out. It is demonstrated that the solution of the obtained polynomial equation is equivalent to finding the inverse of the Brillouin function explicitly.