Abstract
The isotropic Hamiltonian is considered for an open linear chain of -dimensional vector spins ; reduces to the Ising, planar, and Heisenberg models for . The thermodynamic properties (including the susceptibility) of are found for ferromagnetic () and antiferromagnetic () exchange interactions for all temperatures and all spin dimensionalities . The manner in which the various properties depend upon and is studied; in particular we find (a) that although the chain of spins does not display long-range order except at for any value of most of the properties vary monotonically with (in such a way that, e.g., the degree of "short-range order" decreases with increasing ; and (b) that as the spin dimensionality increases without limit, all of the calculated properties approach precisely those predicted by the Berlin-Kac spherical model.
- Received 6 September 1968
DOI:https://doi.org/10.1103/PhysRev.179.570
©1969 American Physical Society