Phases of the hardplate lattice gas on a threedimensional cubic lattice
Abstract
We study the phase diagram of a system of $2\times 2\times 1$ hard plates on the three dimensional cubic lattice, {\em i.e.} a lattice gas of plates that each cover a single face of the cubic lattice and touch the four points of the corresponding square plaquette. We focus on the isotropic system, with equal fugacity for the three orientations of plates We show, using grand canonical Monte Carlo simulations, that the system undergoes two densitydriven phase transitions with increasing density of plates: first from a disordered fluid to a layered phase, and second from the layered phase to a sublattice ordered phase. In the layered phase, the system breaks up into occupied bilayers or equivalently slabs of thickness two along one spontaneously chosen cartesian direction, with a higher density of plates occupying these bilayers relative to the density in the adjacent unoccupied bilayers. In addition to breaking of lattice translation symmetry along one cartesian direction, the layered phase additionally breaks the symmetry between the three types of plates, as two types of plates, with normals perpendicular to the layering direction, have a higher density compared to the third type. Also, the occupied bilayers of the layered phase have powerlaw columnar correlations within each bilayer, corresponding to powerlaw twodimensional columnar order within the occupied bilayers. In contrast, interbilayer correlations of the twodimensional columnar order parameters decay exponentially with the separation between the bilayers. In the sublattice ordered phase, there is twofold ($Z_2$) breaking of lattice translation symmetry along all three cartesian directions. We present evidence that the disordered to layered transition is continuous and consistent with the threedimensional $O(3)$ universality class, while the layered to sublattice transition is discontinuous.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.02611
 Bibcode:
 2021arXiv210902611M
 Keywords:

 Condensed Matter  Statistical Mechanics