Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction

The two-dimensions XY model, undergoes the Berezinskii Kosterlitz Thouless (BKT) transition through unbinding of defect pairs of opposite signs. When the interaction between spins is purely ferromagnetic, these defects have +-1 charge, whereas for pure nematic interaction between spins, they have charge +-1/2. Two-dimensional XY-model in the presence of both ferromagnetic and nematic interactions has been studied both theoretically and experimentally. In this paper, we have studied dynamics of defects in the presence of both ferromagnetic and nematic interactions on a square lattice. Varying the strength of ferromagnetic and nematic interactions, we have observed behavior of both integer and half integer defects and based on that we propose a phase diagram which exhibit three distinct regions in the phase diagram below the critical TBKT : polar phase, nematic phase and coexistence phase and a disordered regions above it. Also, for pure polar and pure nematic case, our results show that the exponent, for algebraic decay of number of defects with time, decays linearly with temperature