Spinodals and transfer matrices in d=1 models

A transfer-matrix method is used to study metastability with particular emphasis on the classical spinodal present in d=1 models when the interaction range goes to infinity. The ‘‘constrained’’ free energy and magnetization as a function of the external magnetic field is found for a number of models. The spinodal is found to be at the magnetic field where the metastable phase encounters a density of eigenvalues which approaches infinity as the interaction range approaches infinity.