Statistical mechanics of one-dimensional Ising and Potts models with exponential interactions

This paper continues the authors' work on a new method for discussing one-dimensional systems in statistical mechanics with exponentially decreasing interactions. It is shown how in the case of the S-spin Ising and the N-state Potts model the results in the classic paper of Kac et al. for these models emerge also from our method. It is the aim of the present paper to compare these two mathematically completely different methods and prepare the extension of our method to two-dimensional systems.