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Based on the method of Dyson–Maleev mean-field theory, we study the Heisenberg ferrimagnetic spin chain at zero temperature. The energy spectrum exhibits the coexistence of a nearly gapless branch and a gapful branch. Compared with numerical results of other methods, the energy gap, Δ h = 1.32 , of Dyson–Maleev mean-field theory is reasonable and only a little bit lower. At finite temperature, the properties of energy gap, magnetization, uniform susceptibility, internal energy, specific heat are calculated respectively. The trends of these thermodynamic properties in this method are consistent with the existed results of other methods. [ABSTRACT FROM AUTHOR]

We use bond operator method to study the dimerized ferrimagnetic spin chain. With the dimerization parameter g from 1 to 0, the model describes the system from normal ferrimagnetic state to dimer state. From the energy spectrums, the system energy is changed from ferrimagnetic spectrum to large energy gap at bond state. At finite temperature, the uniform susceptibility, internal energy and specific heat are calculated respectively with different dimerization parameters g . These results qualitatively agree with the numerical results of other methods quite well. [ABSTRACT FROM AUTHOR]

• The thermodynamic properties of anisotropy ferrimagnetic chain with bond alternation were studied. • At Heisenberg point, the energy gap between two branches is 1.7641, free energy is -1.4659 and ground-state energy is -0.7326. • The effect of anisotropy and bonding alternation on thermodynamic quantities are consistent with other establish methods. We investigate the finite temperature properties of anisotropic ferrimagnetic chain with bond alternation. The spin excitation spectrum as well as the thermodynamic quantities are calculated by means of the extended self-consistent mean-field theory. Two branches of energy spectrum are obtained and the energy gap between them is 1.7641 at zero temperature which agrees quite well with other numerical results. The contribution of bonding alternation δ , anisotropy λ and magnetic field H to the energy gap are present in this research. The other thermodynamic quantities varying with δ and λ , such as ground state energy e , free energy f , specific heat c m , magnetization m and uniform magnetic susceptibility T χ u n i / N g 2 are explicitly discussed, respectively. At Heisenberg point, the e 0 is -0.7326 and f 0 is -1.4659 at zero temperature in this work are reasonable compared with the results calculated by other methods. The effect of λ and δ on the thermodynamic quantities at finite temperature are also well consistent with other established methods. [ABSTRACT FROM AUTHOR]