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

Aleksandar Donev, Joshua Burton, Frank H. Stillinger, and Salvatore Torquato
Phys. Rev. B 73, 054109 – Published 24 February 2006

Abstract

Previous Monte Carlo investigations by Wojciechowski et al. have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.

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  • Received 22 August 2005

DOI:https://doi.org/10.1103/PhysRevB.73.054109

©2006 American Physical Society

Authors & Affiliations

Aleksandar Donev1,2, Joshua Burton3, Frank H. Stillinger4, and Salvatore Torquato1,2,4,*

  • 1Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
  • 2PRISM, Princeton University, Princeton, New Jersey 08544, USA
  • 3Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 4Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

  • *Electronic address: torquato@electron.princeton.edu

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Vol. 73, Iss. 5 — 1 February 2006

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