The isotropic Hamiltonian ${\mathcal{H}}^{(\ensuremath{\nu})}=\ensuremath{-}J\ensuremath{\Sigma}{j=1}^{}^{N\ensuremath{-}1}\mathrm{S}_{j}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{j+1}$ is considered for an open linear chain of
N $\ensuremath{\nu}$-dimensional vector spins
Sj;${\mathcal{H}}^{(\ensuremath{\nu})}$ reduces to the
S=21 Ising, planar, and Heisenberg models for $\ensuremath{\nu}=1,2,\mathrm{and} 3$. The thermodynamic properties (including the susceptibility) of ${\mathcal{H}}^{(\ensuremath{\nu})}$ are found for ferromagnetic (
J>0) and antiferromagnetic (
J<0) exchange interactions for all temperatures
T and all spin dimensionalities $\ensuremath{\nu}$. The manner in which the various properties depend upon
T and $\ensuremath{\nu}$ is studied; in particular we find (a) that although the chain of spins does not display long-range order except at
T=0 for any value of $\ensuremath{\nu}$ most of the properties vary monotonically with $\ensuremath{\nu}$ (in such a way that, e.g., the degree of "short-range order" decreases with increasing $\ensuremath{\nu}$; 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.
The exact solution of the distorted diamond Ising–Hubbard chain is analyzed in the special limit of infinite on-site electron-electron repulsion, where the two-electron Hubbard dimer becomes equivalent to the antiferromagnetic isotropic Heisenberg dimer. The special limit of infinite repulsion for the matrix of the cell Hamiltonian of this model is analytically calculated, and it is demonstrated that the exact solution of the distorted diamond Ising–Hubbard chain in this limit coincides with the exact solution of the spin-1/2 distorted diamond Ising–Heisenberg chain with antiferromagnetic isotropic Heisenberg interaction. The numerical calculation of the special limit of infinite repulsion for the ground-state phase diagram and thermodynamic characteristics of the distorted diamond Ising–Hubbard chain was performed in a way that provides a very fast convergence to the limit results for these characteristics.