Eur. Phys. J. B (2015) 88: 133
https://doi.org/10.1140/epjb/e2015-60210-7

Regular Article

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

^a e-mail: joyjit@imsc.res.in

Received: 29 January 2015
Received in final form: 16 March 2015
Published online: 25 May 2015

Abstract

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.