Soluble model of interacting classical quadrupoles in one dimension

We solve exactly for the thermodynamic properties of a linear chain of classical spins with near-neighbor bilinear and biquadratic isotropic exchange interactions. At zero temperature the system can be either ordered or disordered, depending on the relative magnitudes and signs of the bilinear and biquadratic exchange. In addition, it is found that at finite temperatures "disorder points" occur, at which the correlation functions change in character from monotonic decreasing functions of distance to oscillatory functions. The disorder points found here are of interest because they occur even though the interactions are restricted to nearest neighbors.