Phase transitions in systems of hard rectangles with non-integer aspect ratio
The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, 600113 Chennai, India
Received: 29 January 2015
Received in final form: 16 March 2015
Published online: 25 May 2015
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2015