Phase transitions in a system of hard rectangles on the square lattice

The phase diagram of a system of monodispersed hard rectangles of size m x mk on a square lattice is numerically determined for m = 2,3 and aspect ratio k = 1,2,...,7. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solidlike phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large k is determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger m and k, showing that for k >= 7, the system undergoes three entropy-driven phase transitions with increasing density. The nature of the different phase transitions is established and the critical exponents for the continuous transitions are determined using finite size scaling.