Behaviour of topological charges in the phase transitions exhibited by two planar lattice models

Monte Carlo simulation has been performed in two planar lattice models to investigate the correlation between the topological charges present in these systems and the phase transitions they exhibit. The models consist of two two-dimensional square lattices with nearest neighbor interactions -P2(cosθ) and -P4(cosθ), respectively, where θ is the angle between the nearest neighbor spins and periodic boundary conditions have been assumed. The former system is known to possess a second order phase transition while the second shows a strongly first order one. Both systems are found to possess topological point defects of strength +1/2 and +1. The later defect is unstable in the P2 model but is stable in the P4 one. The ratios of the amount of charges of the two types are sensitive to the transition temperature in both models but behave in remarkably different ways and a qualitative explanation is offered