Phase transitions in a one dimensional model of a ferromagnet: a transfer-matrix approach

It is shown that a transfer-matrix method provides a particularly direct solution for a ferromagnetic version of a one dimensional model originally invented by Fisher (1967). An essential feature of this model is the many body potential leading to a phase transition. All the thermodynamical properties of the model may be written down once the dominant eigenvalue and eigenvector of the matrix are known; in particular, surface properties may be obtained in terms of the dominant eigenvector. Typical phase diagrams are obtained, and the singularities at the phase boundaries discussed.