Critical packing fraction at the phase separation transition in hard-core mixtures

In this paper, I relate the phase separation transition in binary hard-core mixtures in the limit of small size ratio to a bond percolation transition. It allows to estimate the critical packing fraction at the transition as a function of the size ratio and the composition of the mixture for different shapes of objects. The theoretical predictions are in excellent quantitative agreement with numerical simulations of binary parallel hard squares mixtures.