Phase transition in Y-shaped particles on triangular lattice

We study different phases and transitions for the system of Y-shaped particles which are observed in many physical systems such as, igG in human blood, trinapthylene in NOR logic gate etc.

We consider Y-shaped particles on a triangular lattice with only excluded volume interaction among the particles. Two types corresponding to two different orientations of particle are possible. We show that the system undergoes two transitions with increasing the particle density. At low density the system is in a disordered phase, in which both types of particles are present with same fraction and there is no positional order. With increasing particle density the system undergoes a phase transition in which the symmetry in number density of two types of particles is broken. By dividing the triangular lattice into four appropriate sublattices, we observe a sublattice-ordering in this phase. At very high density the system enters into a columnar phase in which only two sublattice densities are high but the symmetry in number density of two types of particles is restored. We show that both transitions are first order in nature. We also show that a simplified system with only one type of particles undergoes a single discontinuous disordered-sublattice transition with increasing particle density.