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Abstract
A spin-1 or three state system will undergo a first or second order phase transition depending on the ratio of coupling parameters α. Using the pair correlation approximation, the transition temperature is determined in order to establish the unstable, the metastable, as well as the stable regions of this cooperative system. The dynamics of the system is studied by means of the most probable path method and the flow lines and fixed points of the system are given for zero field. The choice of possible initial conditions is discussed. The role of the unstable points in the phase diagram, as separators between the stable and metastable points, is described, and they are computed for a number of cases.
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