Thermodynamics of the quantum spin-S XXZ chain

The thermodynamics of the spin-S anisotropic quantum XXZ chain with arbitrary value of S and unitary norm, in the high-temperature regime, is reported. The single-ion anisotropy term and the interaction with an external magnetic field in the z-direction are taken into account. We obtain, for arbitrary value of S, the β-expansion of the Helmholtz free energy of the model up to order β 6 and show that it actually depends on $\frac{1}{S(S+1)}$ . Its classical limit is obtained by simply taking S→∞. At h=0 and D=0, our high temperature expansion of the classical model coincides with Joyce’s exact solution [11]. We study, in the high temperature region, some thermodynamic quantities such as the specific heat and the magnetic susceptibility as functions of spin and verify for which values of S those thermodynamic functions behave classically. Their finite temperature behavior is inferred from interpolation of their high- and low-temperature behavior, and shown to be in good agreement with numerical results. The finite temperature behavior is shown for higher values of spin. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005