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Static Properties of the One-Dimensional Planar Ferromagnet in an External Field

The thermodynamic functions and the correlation length of the classical one-dimensional X Y model in an external field are calculated by the numerical integration of the transfer matrix equation in both ferroand anti ferromagnetic cases. We show that for a finite but weak magnetic field the low temperature structure of the ferromagnetic partition function consists of a spin-wave part and a factor corresponding to the interaction of topological excitations. The contributions of the soliton like topological objects to the static properties are calculated through a systematic perturbative method. Finally we discuss in detail the regions of validity of different analytical approaches by comparing them with our exact numerical solution.