Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets composed of two different spins
(S1,S2) in the elementary cell. It is shown that the spin-wave theory can produce precise quantitative results for the low-energy excitations. The spin-stiffness constant ${\ensuremath{\rho}}_{s}$ and the optical magnon gap $\ensuremath{\Delta}$ of different
(S1,S2) ferrimagnetic systems are calculated, respectively, to second and third order in the quasiparticle interaction. The spin-wave results are compared with available numerical estimates.
We use the mean-field approximation of Dyson–Maleev representation to study an XXZ Heisenberg ferrimagnetic spin chain with single-ion anisotropy. By solving the self-consistent equations with different anisotropies, λ and D respectively, the energy spectrums, internal energy, static susceptibility and specific heat are calculated. Especially, the quantum phase transition of the magnetization plateau induced by single-ion anisotropy D is obtained in the model of the ferrimagnetic spin chain by using Dyson–Maleev mean-field theory.
The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S ′) SU(2) operator interacting with a XXZ like interaction (anisotropy ∆). Our results indicate universal properties for all these chains. The whole phase, 1> ∆> −1, where the models change from ferromagnetic ( ∆ = 1) to ferrimagnetic ( ∆ = −1) behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions. 1