Quantum spherical spin model on the A B2 chain

A quantum spherical spin model with an antiferromagnetic coupling J on the AB₂ chain is studied, whose topology is of interest in the context of ferrimagnetic polymers and oxocuprates. A ferrimagnetic long-range order is found at the only critical point g=T=h=0 , where T denotes the temperature, h the magnetic field, and g the quantum coupling constant in energy units. The approach to the critical point, with diverging correlation length ξ and cell susceptibility χ_cell , is characterized through several paths in the {g,T,h} parameter space: for (T/J)→0 and g=h=0 , χ_cell∼1/T² , as also found in several classical and quantum spherical and Heisenberg models; for (h/J)→0 and g=T=0 , χ_cell∼1/h ; and for (g/J)→0 and T=h=0 , lnχ_cell∼1/g , thus evidencing an essential singularity due to quantum fluctuations. In any path chosen the relation χ_cell∼ξ² is satisfied. For finite g and T a field-induced short-range ferrimagnetism occurs to some extent in the {g,T,h} space, as confirmed by the analysis of the local spin averages, cell magnetization with a rapid increase for very low fields, and spin-spin correlation functions. The asymptotic limits of the correlation functions are also provided with respect to g , T , h , and spin distance. The analysis of the entropy and specific heat reveals that the quantum fluctuations fix the well-known drawback of classical spherical models concerning the third law of thermodynamics.