Effect of long-rang interactions on the Kosterlitz-Thouless transition
The two-dimensional XY model of continuous spins on a square lattice is studied by Monte Carlo simulations in the nonextensive statistical approach of Tsallis, using the Metropolis algorithm with a transition probability of the nonextensive approach. Energy per spin, magnetization per spin, heat capacity, magnetic susceptibility, Binder cumulant of the magnetization and Binder cumulant of the energy are calculated in a temperature interval between 0.02 and 2 with a step of 0.02, for square lattice sizes considered between 122 and 482, with periodic boundary conditions, and for discrete values of the Tsallis entropic index q used between 0.99 and 0.5. It has been found that the Kosterlitz-Thouless transition is well observed and modified for q=0.99 and 0.9 ; its critical temperature decreases when q decreases. A particular behavior of the system evolution is observed for q=0.8 and 0.7. The absence of phase transitions was confirmed for q ≤ 0.6.