A multiple occupancy cell fluid model with competing attraction and repulsion interactions

An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie-Weiss-type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral representation of the grand partition function, we apply Laplace's method to obtain asymptotically exact expressions for the pressure, density and equation of state. The model exhibits a hierarchy of first-order transitions, each terminating at a critical point. We determine the coordinates of the first five such points. Recasting the formalism in dimensionless variables highlights the explicit temperature dependence of all thermodynamic functions. This enables us to derive a closed-form expression for the entropy. The results reveal pronounced entropy minima around integer cell occupancies and reproduce density-anomaly isotherm crossings analogous to those in core-softened models.