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Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have foundtwo unusual phases in two-dimensional systems of anisotropic hard particles: atetratic phase of four-fold symmetry for hard squares [Comp. Methods in Scienceand Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase forhard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, westudy a system of hard rectangles of aspect ratio two, i.e., hard-square dimers(or dominos), and demonstrate that it exhibits a solid phase with both of theseunusual properties. The solid shows tetratic, but not nematic, order, and it isnonperiodic having the structure of a random tiling of the square lattice withdominos. We obtain similar results with both a classical Monte Carlo methodusing true rectangles and a novel molecular dynamics algorithm employingrectangles with rounded corners. It is remarkable that such simple convextwo-dimensional shapes can produce such rich phase behavior. Although we havenot performed exact free-energy calculations, we expect that the random dominotiling is thermodynamically stabilized by its degeneracy entropy, well-known tobe $1.79k_{B}$ per particle from previous studies of the dimer problem on thesquare lattice. Our observations are consistent with a KTHNY two-stage phasetransition scenario with two continuous phase transitions, the first fromisotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio

Tetratic order in the phase behavior of a hard-rectangle system