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Monte Carlo study of hard pentagons

Tanja Schilling*, Sander Pronk†, Bela Mulder, and Daan Frenkel

  • FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands

  • *Current address: Institut für Physik, Johannes Gutenberg-Universität D-55099 Mainz, Germany.
  • †Current address: Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
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Phys. Rev. E 71, 036138 – Published 25 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036138

Abstract

How does a liquid freeze if the geometry of its particles conflicts with the symmetry of the crystal it should naturally form? We study this question in the simplest model system of particles exhibiting such a symmetry mismatch: hard pentagons in two dimensions. Using isobaric and isotensic Monte Carlo simulations we have studied the phase behavior of hard pentagons. On increasing the pressure from the homogeneous and isotropic low-density phase, the system first exhibits a rotator phase (plastic solid) with a triangular lattice structure. At higher densities it undergoes a weak first-order phase transition into a “striped” phase composed of alternating rows of oppositely pointing particles. This phase is analogous to the “striped” phase in the compressible antiferromagnetic Ising model on a triangular lattice and is an example of systems in which frustration due to the mismatch in symmetries is released by an elastic coupling to the lattice. In order to pursue this analogy we also consider hard heptagons, showing that in this case the decrease in symmetry mismatch indeed leads to a shift in the transition densities to higher values and a weakening of the transition.

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Phys. Rev. E 71, 036138– Published 25 March, 2005
  • Received 1 November 2004

© 2005 American Physical Society

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