Diagram Technique for Spin-Operators and Its Applications to Some Problems of Ferromagnetism

Abstract

A diagram technique for calculation of correlation functions of ferromagnet being described by the Ising model is proposed here and its zero approximation corresponds to the selfconsistent field. The essential dependence of a numerical factor of a diagram upon its structure is the important peculiarity of this technique in comparison with the usual diagram technique for fermion or boson operators. It leads to the special character of analytical series corresponding to the certain diagram series and to the special ways of their summarizing. The exact forma1 expression for the average spontaneous moment in terms of irreducible many-particle correlation functions had been obtained. A certain series of graphs for spontaneous moment which corresponds to the Gaussian fluctuations of the selfconsistent field being taken into account had been extracted. A relation between the proposed diagram technique and the expansion of functional integrals for the correlation functions of the Ising model had been obtained as well. In conclusion the referencies to authors papers where a diagram technique for Heisenberg and s-d models are developed are given there

Pseudospin-Electron Model at Weak Coupling

“…Calculating the mean values of the T τ -products of the pseudospin and the electron operators we use the diagrammatic techniques based on the Wick's theorem for the spin operatoes [23] (besides the usual procedure for the Fermi operators). After elimination in this way of the nondiagonal σ ± operators we perform the semi-invariant expansion in order to calculate the mean values of the remaining products of the σ z operators.…”

To the Theory of Relaxation Phenomena in Quasi-One-Dimensional Ferroelectrics With Hydrogen Bonds. Nonequilibrium Statistical Operator Approach

“…The both approaches give numerically close results. For the description of experimental data within the NSO method one must calculate kinetic parameters K (2) µ and K (1) . In the course of such a calculation one must consider mechanisms of relaxation in given crystals.…”

“…Thus, the TCA algorithm leads to a system of nonlinear differential equations (3.12), (3.13) for variables η (1) , η (2) , ∆. This system seems to be quite intractable.…”

“…To describe the property of some compound on the basis of the obtained above results one has to consider a mechanism of relaxation of that compound and calculate the kinetic parameters K (2) µ and K (1) . We shall not discuss this problem here.…”

“…[1][2][3][4][5][6][7][8]. In the case of low-dimensional structures, the model allows an accurate calculation of the thermodynamic quantities (order parameters, static susceptibility, specific heat) and the spin correlation functions [7][8][9].…”