Solitonic elliptical solutions in the classical XY-model

The solitonic-like solutions predicted by the continuum semi-classical two‐dimensional XY -model are investigated using canonical Monte Carlo simulation. In particular, we verify the existence of kink states, and study their degree of stability. These states, that were supposed to exist from approximate theories applied to the continuum limit of this model, are a new kind of solution of the XY model under external magnetic field. In the simulation several system sizes up to 100◊100 spins were considered. The study of the static spin correlation between the initial and final configuration shows there exist a finite transition temperature Tc, which is independent of the system size. According to our simulation, at T < Tc the kink state is stable, and the degree of stability increases with system size.