Thermodynamics of alternating (s,s’) chains in the nearest-neighbor Ising-model approximation

The exact solutions of the so-called (1/2,s’ ${)}_{\mathit{N}}$ ferrimagnetic z-z chain made up of two sublattices have been previously derived by using the transfer-matrix method. In this paper, we generalize this method to (s,s’ ${)}_{\mathit{N}}$ chains, with arbitrary s and s’. We give a general expression for the correlation length ξ and the product ${\mathrm{\chi }}_{\mathrm{\parallel }}$T in the low-temperature range. We specifically discuss the case of the moment-compensated chain in the low-temperature limit and generalize the results previously obtained. We show that, in this limit, the chain behaves as an assembly of quasi-independent, quasirigid blocks, each with length ξ, and that, in the low-temperature range, the product ${\mathrm{\chi }}_{\mathrm{\parallel }}$T behaves as ξ${\mathit{M}}^2$, with M the thermal-average magnitude of the magnetic moment attributed to the unit cell.