Weakly first-order transition in an athermal lattice gas

We investigate the phase behavior of a two-dimensional athermal lattice gas in which every hardcore particle can have two or fewer nearest neighboring occupied sites on the square lattice. The ground state and close packing density are determined and it is found that at large chemical potential the model undergoes an ordering phase transition with preferential sub-lattice occupation. Although near the transition point the particle density and entropy exhibit an apparent discontinuity we find that the order parameter and fluctuations of thermodynamic quantities do not scale with the system volume. These paradoxical results are reconciled by analyzing the size dependent flow of the thermal exponent by phenomenological renormalization and the curve-crossing method, which lead to a weakly first-order phase transition scenario.