Inequivalence of statistical ensembles in rod-like chains on a one-dimensional lattice

In this work we study a three-state model which has exact solutions in the microcanonical and grand-canonical ensembles showing an inequivalence of statistical ensembles for small systems. We consider N chains placed on an unidimensional lattice, such that each site may assume one of three-states: empty (state 1), with a single molecule energetically null (state 2), and with a single molecule with energy ε (state 3). Each molecule consists of two monomers connected one to each other by a rod.