Spin waves in 2D classical XY-model

The description of phase transition in the microcanonical formalism has gained growing interest in recent years for the calculation of thermostatic properties of physical systems and microcanonical entropy.$^{1}$ We have carried out micro-canonical Monte Carlo simulations of the 2D XY-model using periodic boundary conditions.$^{2,3}$ In case of microcanonical Monte Carlo simulation some thermodynamic-like relations apply that allow definition of variable by averaging, specifically, the temperature. The energy distributions of the spins have been obtained for the the Kosterlitz-Thouless situation.$^{4}$ In this case, the energy distribution of vortices show features that is due to spin waves, which agrees with the spin wave theory which predicts that E$_{sw}$=-2+T/2. References: [1] H.Behringer and M.Pleimling, Phys.Rev.E \textbf{74} (2006) 11108 [2] M.Creutz, Phys.Rev.Lett. \textbf{50} (1983) 1411 [3] S Ota and S B Ota, Phys.Lett.A \textbf{367} (2007) 35 [4] J B Kogut, Rev.Mod.Phys. 51 (1979) 659