Ordered metastable states in the Potts model and their connection with the superheated solid state

In this work we study the ordered metastable state in a two-dimensional Potts lattice in the microcanonical ensemble under the conditions for first-order transitions. We connect our results with the melting transition in solids, and in particular with the empirical findings of the Z-method. In contrast with the sharp, discontinuous slope of the isochoric curve observed in the melting of solids, an S-shape curve is observed for T(E) in the case of spins. We discuss the implications of our results to extend the Z-method and its applicability for general first-order phase transitions.