Phase transitions in systems of hard rectangles with non-integer aspect ratio

We investigate, using Monte Carlo simulations, the phase diagram of a system of hard rectangles of size m × mk on a square lattice when the aspect ratio k is a non-integer. The existence of a disordered isotropic phase, a nematic with only orientational order, a columnar phase with orientational and partial translational order, and a high density phase with no orientational order is shown. The high density phase is a solid-like sublattice phase only if the length and width of the rectangles are not mutually prime, else, it is an isotropic phase. The minimum value of k beyond which the nematic and columnar phases exist are determined for m=2 and 3. The nature of the transitions between different phases is determined, and the critical exponents are numerically obtained for the continuous transitions. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015