The phase diagram of the spin-1 Blume-Cape1 model in a random crystal field di obeying a two-valued distribution P(di) = p 6(di -d) + (1 -p ) 6(di) has been studied by the two-spin cluster expansion. In a previous investigation [l, 21 the phase diagram of this model with a random crystal field has been obtained within the mean-field approximation (MFA). In this note we study, via a two-spin cluster in the cluster expansion theory (CE) originally due to Strieb et al. [3], the influence of crystal-field disorder on the (d, T ) phase diagram at a given concentration p .The reduced (divided by p-' = kT) Hamiltonian of the system is given by where K = p J > 0, Sf = 0, + 1, J is the exchange parameter, and h is the external magnetic field. The first summation is over all nearest-neighbor pairs and the second summation is over all the lattice sites. The phase diagram of this model is determined by calculating the contributions to the free energy up to two-spin cluster in the CE theory. The average free energy per site is given byS is the internal-field parameter which describes the long-range order and whose best value is determined by minimizing the free energy.') Moyzesova 16, 04001 KoSice, Slovak Republic.
The reorientation temperature in ultrathin ferromagnetic films is studied within the framework of the many‐body Green function theory. The model Hamiltonian includes a Heisenberg term with the different surface exchange couplings with respect to the bulk one, a second‐order single‐ion anisotropy, and a transverse external magnetic field in the x‐direction. The single‐ion anisotropy term is treated by the generalized Anderson–Callen decoupling scheme. We investigate the reorientation temperature TR (a) as a function of the surface single‐ion anisotropic parameter K2,S(T → 0) for different: film thicknesses L, surface exchange coupling enhancements ΔS, transverse magnetic fields h and (b) as a function of the transverse magnetic field h for different: film thicknesses L, surface exchange coupling enhancements ΔS, surface single‐ion anisotropic parameters K2,S(T → 0).
The two-dimensional (2D) Heisenberg model with spin S = 1, with the exchange anisotropy plus a second-order uniaxial single-site anisotropy and an external transverse magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the expectation values Sof the spin components from which the orientation angle θ is obtained as a function of the temperature and of the transverse magnetic field for various parameters of the exchange anisotropy in the (x,y)-plane.
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