Thermodynamics of alternating quantum-classical spin chains with ZZ-type couplings and/or cations randomly distributed

Abstract

We propose a general treatment for solving the case of ferrimagnetic chains made up of two sublattices (S,s) and characterized by ZZ exchange couplings between nearest neighbors and/or cations randomly distributed. We use the technique of transfer matrix. We show that it is only possible to have simple closed-form expressions for the zero-field partition function and for the parallel and normal susceptibilities if s = 1 2 . Then we restrict our study to the case of randomly distributed exchange energies; more particularly, we examine two cases of physical interest: (i) the exchange energies can take negative but also positive values independently (chains characterized by a mixture of ferromagnetic and antiferromagnetic couplings, respectively); (ii) these energies have always the same sign but take different values independently (purely ferromagnetic or antiferromagnetic coupled chains). However, the problem of cationic vacancies is briefly examined. We detail the low-temperature behaviors of the susceptibilities and we compare the results to those ones previously obtained for chains showing isotropic coupling randomly distributed.