Phonon Scattering by Paraelectrical Centers in Crystals I. General

On the Relaxational Properties of a Quantum Dipolar Spin Glasses Model

“…f  of random mean fields Λ i was considered in papers [8,9,18]. We note that the introduction of the random field Λ i with some distribution function   i f  allows the many-particle problem to lead to one particle unperturbed random Hamiltonian 0 and the perturbation W. For random system like spin glass the equivalence of the configurational average to the average over random molecular fields with distribution function, is usually used [8,9,18].…”

“…This expression results from the spectral representation for the Fourier components of the Green function (9) which are analytically continued an all complex plane. The calculation of   ij G  is performed using diagrammatic technics developed in ref.…”

“…We note that the introduction of the random field Λ i with some distribution function   i f  allows the many-particle problem to lead to one particle unperturbed random Hamiltonian 0 and the perturbation W. For random system like spin glass the equivalence of the configurational average to the average over random molecular fields with distribution function, is usually used [8,9,18]. Klein et al [18] consider a self-consistent mean random field approximation in spin glass theory which leads to sharp phase transition in the Sherrington-Kirkpatrick theory if the coordination number .…”

“…In ref. [8,9] we derived the non linear integral equation for distribution function f(Λ) of the form, [18]. The expression for moments [8,9,18] include the parameters,…”

“…The problem remain open. Finally we note that the some kind of questions arise when we investigate dipolar pseudo spin glasses model with electric impurity dipolar centers in crystals or the role of the strong interactions between the elastic tunneling defects like the two-level system (TLS) in glass [8][9][10][11][12][13][14]. In this paper the magnetic dynamical susceptibility of dipolar spin glass in a transverse field is theoretically considered.…”