THEORY OF THE MAGNETIC-PROPERTIES OF AN INFINITE CLASSICAL SPIN-CHAINSHOWING AXIAL ANISOTROPIC COUPLINGS - LOW-TEMPERATURE BEHAVIOR

We consider a classical spin chain characterized by axial anisotropic couplings between nearest neighbors. In particular the antisymmetrical part of exchange is taken into account by means of a Dzialoshinski co upling characterized by a regular or an alternate direction from pair to pair. We expand each operator exp(-betaH(i)) on the infinite basis of spheroidal functions. We show that the zero-field partition functio n Z(N)(0) has a closed-form expression. The spin-spin correlations can be derived as well as the susceptibilities chi(uu) (with u=x or y) an d chi(zz) We achieve a thorough investigation of the chain low-tempera ture behaviors. It appears that there are predictable and original beh aviors. In particular, when the z axis is favored, the lowest-energy c onfiguration corresponds to a ferromagnetic or an antiferromagnetic ar rangement, with the spins lying along this axis. When the X-Y plane is favored, the spins lie within this plane and exhibit a ferromagnetic, an antiferromagnetic, a helical, or a canted structure. Finally, we p oint out interesting crossover phenomena, but they are not discussed i n detail.