Spin‐one Ising model with biquadratic exchange interaction within functional integration method

Abstract

A spin-one Ising model with biquadratic exchange interaction is investigated within a functional integration approach. The phase diagram is analyzed by means of Landau's free energy expansion. The dependence of the features of the system on the ratio of bilinear to biquadratic exchange interaction constants is discussed. In the random phase approximation, expressions for phase transition temperatures and the tricritical point for the ferromagnetic transition are obtained. Mogenb k l 3 l i H r a C 6MKBaupaTHbIM 06MeHHbIM B3aIlMOAekTBMeM (UnH s = 1) Kiy%XTCX B PaM-KaX MeTOAa @YHK4XOHaJIbHOrO MHTerpMpOBaHMX. @a30BaH RMarpaMMa aHa.JlH3Up)'eTCX IIpM IIOMOWli pa3JlOXeHHH . b H u a y CBO6OuHOfi 3HePrMli. PaCCMOTpeHa 3aBMCMMOCTb CHCTeMbI OT OT-HOIIIeHIllI B e n H W H 6 w n u~e i~o r o M 6 M K B a~p a T H O r O 06MeHHbIX B3aHMORekTBHb. B npn6nme-TMW3CKOJ% TOgKIl @eppOMarHMTHOrO IIepeXOUa.

Disordered spin‐one Ising model with biquadratic exchange interaction within functional integration method

“…Necessary functional integrals can be found by expansion over the Gaussian moments considering the non-Gaussian part as a small perturbation. We have obtained the expression for the free energy in the approximation of "two sums over k (see [7]), but it is too cumbersome to be presented here. In RPA, The formalism developed above can be used for the analysis of the well-known quadrupolar glass model (LRT model) introduced in 191.…”

“…However, the study of disordered systems of that kind is so far in embryonic state. Continuing our recent investigation of the spin-one king model with biquadratic exchange [3] we shall consider now structurally disordered system.…”

“…(see equations (1.18) to (1.22) of[3]; finally, the renormalized interactions are Expression (19) corresponds to the first order of perturbation theory over the cube of the inverse effective exchange interaction range rO3 proposed in[8], which in the case of a disordered system is defined byr i 3 = (4n(g)3'2 N/3V)-', where & = J dRR2J(R)/J d R J(R).4. Random Phase ApproximationLet us find expressions for the transition temperatures in RPA.…”

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

“…The superexchange between these unquenched orbital momentum gives rise to a biquadratic exchange interaction term in the Hamiltonian [4]. Other interactions such as phonon exchange between ions [5] and the Schrodinger's spin-one exchange operator [6] can also result in the inclusion of such interaction. Both attractive and repulsive biquadratic interactions are of interest.…”

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

“…biquadratic) as well as of a non-exchange (e.g. single-ion anisotropy) origin on the physical properties of the systems [4][5][6][7][8][9][10][11][12][13].…”