Classical one-dimensional Heisenberg model with an interaction of finite range

It is shown that the thermodynamic quantities and spin correlation functions of the classical Heisenberg model on a linear chain are expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of a homogeneous linear integral equation, where the range of the interaction is assumed to be finite. The magnetization and susceptibility at nonzero external magnetic fields are given as a function of temperature, for the case of the nearest neighbour ferromagnetic and antiferromagnetic interaction. Efforts are paid to determine the properties near zero temperature.