We study the k-NN hard-core lattice gas model in which the first k next-nearest-neighbor sites of a particle are excluded from occupation by other particles on a two-dimensional square lattice. This model is the lattice version of the hard-disk system with increasing k corresponding to decreasing lattice spacing. While the hard-disk system is known to undergo a two-step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high-density expansions of the free energy and density, we argue that for k = 4,10,11,14,⋯, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for k = 4,...,11. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first-order transition.

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.

Lattice theory and statistics PACS 64.60.De -Statistical mechanics of model systems PACS 64.60.Bd -General theory of phase transitionsAbstract -A system of 2 × d hard rectangles on square lattice is known to show four different phases for d ≥ 14. As the covered area fraction ρ is increased from 0 to 1, the system goes from low-density disordered phase, to orientationally-ordered nematic phase, to a columnar phase with orientational order and also broken translational invariance, to a high density phase in which orientational order is lost. For large d, the threshold density for the first transition ρ * 1 tends to 0, and the critical density for the third transition ρ * 3 tends to 1. Interestingly, simulations have shown that the critical density for the second transition ρ * 2 tends to a non-trivial finite value ≈ 0.73, as d → ∞, and ρ * 2 ≈ 0.93 for d = 2. We provide a theoretical explanation of this interesting result. We develop an approximation scheme to calculate the surface tension between two differently ordered columnar phases. The density at which the surface tension vanishes gives an estimate ρ * 2 = 0.746, for d → ∞, and ρ * 2 = 0.923 for d = 2. For all values of d, these estimates are in good agreement with Monte Carlo data.

Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations in aspect-ratio, quite contrary to what is known from frictionless systems. arXiv:1812.00757v1 [cond-mat.soft]

We study a system of monodispersed hard rectangles of size m×d, where d ≥ m on a two dimensional square lattice. For large enough aspect ratio, the system is known to undergo three entropy driven phase transitions with increasing activity z: first from disordered to nematic, second from nematic to columnar and third from columnar to sublattice phases. We study the nematic-columnar transition by developing a high-activity expansion in integer powers of z −1/d for the columnar phase in a model where the rectangles are allowed to orient only in one direction. By deriving the exact expression for the first d + 2 terms in the expansion, we obtain lower bounds for the critical density and activity. For m, k ≫ 1, these bounds decrease with increasing k and decreasing m.