Effect of long-rang interactions on the Kosterlitz-Thouless transition

Authors

• Yazid Benbouzid * ^{1, 2}
• Slimane Chala ^{3, 4}
• Mostefa Maache ^{1, 5}

1. Physics Department, Ziane Achour University, Djelfa, Algeria
2. Laboratory of Physico-Chemistry of Materials and Environment, Ziane Achour University, Djelfa, Algeria
3. Institute of Electrical and Electronic Engineering, M' Hamed Bougara University, Boumerdes, Algeria
4. Laboratory of Metallic and Semiconducting Materials, Mohamed Khider University, Biskra, Algeria
5. Laboratory of Physics of Thin Films and Applications, Mohamed Khider University, Biskra, Algeria

Abstract

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.

Keywords

• Kosterlitz-Thouless transition
• Monte Carlo simulation
• Tsallis statistics
• Two-dimensional XY model