Freezing in the presence of disorder: a lattice study

We investigate the freezing transition in a two-dimensional lattice model of annealed hard squares that are subject to the influence of randomly placed quenched particles of the same size. The latter model is a porous medium. By combining two recent density functional approaches we arrive at a theory for quenched-annealed lattice fluids that treats the quenched particles on the level of their one-body density distribution. We show that this approach yields thermodynamics that compare well with results from treating matrix realizations explicitly and performing subsequent averaging over the disorder. The freezing transition from a fluid to a columnar phase is found to be continuous. On increasing matrix density it shifts towards close packing and vanishes beyond a threshold matrix density.