Phase transitions in a system of hard Y-shaped particles on the triangular lattice

Abstract

We study the different phases and the phase transitions in a system of Y-shaped particles, examples of which include immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbors chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implement an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solidlike sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite-size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particle undergoes a single discontinuous phase transition from a disordered phase to a solidlike sublattice phase with an increasing density of particles.

Phase transitions in hard-core lattice gases on the honeycomb lattice

“…Therefore, in order to improve our sampling, in the 2NN case we proceed as in Ref. [17] and add a sliding movement in which a linear cluster is formed and slid in a given direction (see Fig. 3 for illustration).…”

“…In Ref. [17], authors hint at a possible columnar phase as a second-order perturbation in a full-packed system of Y -shaped particles on the honeycomb lattice. In their brief discussion, the following scenario is presented: Starting in a solidlike phase at maximum density, first a transition to a columnar phase takes place as density is decreased.…”

“…While some systems have approximate results obtained by means of analytical procedures [9][10][11][12], only the hard hexagons model has an exact solution [13]. Monte Carlo simulations have been used to study several other particle shapes and their mixtures [14][15][16][17][18][19][20][21][22][23], most of them on the square, triangular, or cubic lattices. Recently, a number of models with both symmetrical and asymmetrical particles have been studied in continuous [24] and discrete [16,25,26] space, showing several phase transitions, including high-density columnar phases missed by earlier studies on the square lattice and an hexatic phase on the triangular lattice [27].…”

“…Recently, a number of models with both symmetrical and asymmetrical particles have been studied in continuous [24] and discrete [16,25,26] space, showing several phase transitions, including high-density columnar phases missed by earlier studies on the square lattice and an hexatic phase on the triangular lattice [27]. In contrast to previous approaches, which employed single-particle modifications during sampling, recent studies employ highly efficient cluster algorithms [16,17,19,21,25,26], enabling simulations of systems with up to N = 1024 2 lattice sites. Another very interesting result is the possibility of multiple phase transitions for larger exclusion regions whenever a sliding instability is present at high-density phases [16,17,28].…”

“…In contrast to previous approaches, which employed single-particle modifications during sampling, recent studies employ highly efficient cluster algorithms [16,17,19,21,25,26], enabling simulations of systems with up to N = 1024 2 lattice sites. Another very interesting result is the possibility of multiple phase transitions for larger exclusion regions whenever a sliding instability is present at high-density phases [16,17,28]. Finally, the melting of two-dimensional (2D) materials has also attracted attention lately, undergoing many interesting critical phenomena [29][30][31].…”