Study of the crossover from 2 to 3 dimensions in the quantum spin-12 anisotropic Heisenberg model

The phase diagram of the quantum spin-12 anisotropic Heisenberg antiferromagnet is studied, within a mean-field renormalization-group approach in larger clusters. The model consists of an anisotropic cubic lattice, with in-plane J and inter-plane J′=λJ interactions. The dependence of the Néel temperature TN on the interlayer coupling λ and on the anisotropy parameter Δ (Δ=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively) is obtained explicitly. We have shown that TN(Δ,λ) is different from the Curie temperature Tc(Δ,λ), such that, at Δc(λ) [or λc(Δ)], Tc=TN. The set of points Δc(λ) determine a characteristic frontier in the (λ,Δ) plane, which separate three regimes. These are defined as: Curie, when Tc>TN, Néel, when Tc<TN, and mixed, where the two previous regimes coexist.