Yazid Benbouzid - Physics Department, Ziane Achour University, Djelfa, Algeria
Slimane Chala - Institute of Electrical and Electronic Engineering, M&#۰۳۹; Hamed Bougara University, Boumerdes, Algeria
Mostefa Maache - Physics Department, Ziane Achour University, Djelfa, Algeria

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 ۰.۰۲ and ۲ with a step of ۰.۰۲, for square lattice sizes considered between ۱۲۲ and ۴۸۲, with periodic boundary conditions, and for discrete values of the Tsallis entropic index q used between ۰.۹۹ and ۰.۵. It has been found that the Kosterlitz-Thouless transition is well observed and modified for q=۰.۹۹ and ۰.۹ ; its critical temperature decreases when q decreases. A particular behavior of the system evolution is observed for q=۰.۸ and ۰.۷. The absence of phase transitions was confirmed for q ≤ ۰.۶.

two-dimensional XY model, Kosterlitz-Thouless transition, Tsallis statistics, Monte Carlo simulation