Explicit thermostatics of Stanleyʹs n-vector model on the harmonic chain by Fourier analysis

Thermostatic properties of Stanleyʹs classical n-vector model on the harmonic chain are studied. It is shown that this model belongs to a rather general class of classical spin models in one dimension. The members of this class are characterized by spins which are elements of a homogenous space with transformation group G and a G-invariant and exchange-invariant spin-pair interaction. For the derivation of basic thermostatic quantities and correlation functions we use the method of abstract Fourier analysis. This allows to derive rather explicit results for any member of the aforementioned class of spin models. We present an exact closed-form expression as well as a high- and a low-temperature expansion for the free energy of Stanleyʹs n-vector model on the harmonic chain. From this basic thermostatic quantities like internal energy, entropy and heat capacity are obtained. Furthermore, we present results for expectation values of one-spin and two-spin functions. From the latter it is possible to derive the zero-field susceptibility and it also allows for a discussion of magnetostrictive effects.