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Statistical Perturbation Theory of Order–Disorder Ferroelectrics: Zeroth Approximation
Author(s) -
Nettleton R. E.
Publication year - 1967
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.19670240219
Subject(s) - eigenvalues and eigenvectors , quantum tunnelling , commutator , operator (biology) , physics , quantum mechanics , perturbation theory (quantum mechanics) , order (exchange) , hydrogen atom , perturbation (astronomy) , condensed matter physics , mathematical physics , chemistry , biochemistry , lie conformal algebra , finance , repressor , lie algebra , transcription factor , economics , group (periodic table) , gene
Approximate spin‐wave energies are calculated by constructing approximate eigenvalues of the commutator operator [H, ]. One linearizes commutators by replacing the Z spin operator by its expectation 〈Z〉 and then determines the latter self‐consistently. Such a calculation is discussed for the Blinc formulation of the Slater‐Takagi‐Senko model of KH 2 PO 4 which is treated by a coordinate rotation similar to that used by DeGennes. For sufficiently large tunneling of protons on hydrogen bonds, the rotation angle will approach π/2 at a temperature defining a second‐order transition. If tunneling is weak, the transition is first‐order, unless there is no tunneling. In the latter case, the model reduces to that of the Weiss molecular field, and the transition is again of second order.