Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice

Abstract

We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order k (k = 1 . . . 5) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the 2D-Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high density columnar phase undergoes a first order phase transition with non-standard scaling to a solid-like phase with short range ordered domains and, then, to fluid-like configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the 3-state Potts model. The 5NN system undergoes two first order phase transitions, both with non-standard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice

“…Parallel to the study of models in the continuum, models of hard-core particles on lattices, known as hard core lattice gases (HCLGs) have also been studied. In literature, many different geometrical shapes have been studied in two dimensional lattices, which include triangles [17], squares [18][19][20][21][22][23], dimers [24][25][26][27], Y-shaped particles [28], mixture of squares and dimers [29,30], rods [31,32], rectangles [33][34][35][36], discretised discs or the k-NN model [37][38][39][40][41], hexagons [42], etc., the last being the only exactly solvable model. A variety of different ordered phases may be observed including crystalline, columnar or striped, nematic, power-law correlated phases, etc.…”