First-order transition in 2D classical XY-model

We have carried out micro-canonical Monte Carlo simulations of the extended 2D XY-model in 30$\times $30 lattice using periodic boundary conditions.$^{1-4}$ The energy distributions of the spins have been obtained for the value of the parameter q=55.$^{3,4}$ The energy distribution of the spins in the lattice shows features that can be associated with spin wave and vortex excitations.$^{5}$ The results agree with the first-order transition observed in canonical Monte Carlo simulations, due to vortex nucleation.$^{3}$ References: [1] M.Creutz, Phys.Rev.Lett. \textbf{50} (1983) 1411 [2] S Ota and S B Ota, Phys.Lett.A \textbf{367} (2007) 35 [3] E.Domany, M.Schick, R.H.Swendsen, Phys.Rev.Lett. \textbf{52} (1984) 1535 [4] J.E.van Himbergen, Phys.Rev.Lett. \textbf{53} (1984) 5; Phys.Rev.B \textbf{29} (1984) 6387 [5] J B Kogut, Rev.Mod.Phys. \textbf{51} (1979) 659