Thermodynamics of Interacting Hard Rods on a Lattice

We present an exact derivation of the isobaric partition function of lattice hard rods with arbitrary nearest-neighbor and long-range interactions. Free energy and all thermodynamics functions are derived accordingly, and they are written in a form that is suitable for numerical implementation. As an application, we have considered lattice rods with pure hard-core interactions, rods with long-range gravitational attraction, and finally a charged hard rods with charged boundaries (Bose gas), a model that is relevant for studying several phenomena such as charge regulation, ionic liquids near charged interfaces, and an array of charged smectic layers or lipid multilayers. In all cases, thermodynamic analyses have been done numerically using the Broyden algorithm.