How the overlap of excluded volume determines the configurational energy landscape and “thermodynamics” in the “one to five hard disks in a box” system

In this work, the effects of excluded volume are studied in the “one to five hard disks in a box” system, based in writing an exact equation of state in which the excluded volume overlap is related with the spare volume. For one and two disks in different types of cages, the attractive and repulsive forces are calculated analytically. These attractive forces are due to excluded volume overlap allowing second neighbors to have an effective interaction, a fact that is usually neglected when considering only collisions with first-neighbors. The same effects are observed for numerical computations with five-disks in a box, as the distributions of distances between disks and disks to walls suggest. Also, numerically exact equations of state are presented for the one to five hard disks in a box system from a direct-sampling Monte Carlo procedure. All these results indicate that first and second-neighbor excluded volume interactions are essential to determine the energy landscape topology. This work supports previous observations which suggests that second-neighbor excluded volume interactions in hard-core systems are related with phase transitions.