Frustration in 2D Anti-ferromagnetic Triangular Ising Spin Lattice: A Monte Carlo Study

The Monte Carlo simulation method is used to investigate the magnetic frustration phenomenon for anti-ferromagnetic interactions in a triangular lattice by means of the two dimensional Ising model. Frustration is due to the presence of competing ferromagnetic and antiferromagnetic interactions in this magnetic system, which leads to the fact that the ground state of the system does not correspond to the minimization of each of the interaction energy. Since the energy of the system depends on the order at microscopic level, frustration can lead to disordered states such as spins glasses. Thus, the antiferromagnetic/ paramagnetic (AFM/PM) phase transition is investigated. We showed that the AFM/PM phase transition occurs at the critical temperature, T-N = 1.2 ( in J / k(B) units, where J is the exchange integral and B k(B) Boltzmann's constant). Also, the minimum energy of the system is -1 instead of -3 (in J / k(B)T units) as it was expected for the case of antiferromagnetic interactions on a triangular Ising spin lattice.