Study of the frustration in a 2D square lattice: a Monte Carlo study

In this paper, we study the magnetic properties of a square lattice system in 2D, using Monte Carlo simulations. Firstly, we elaborate the ground state phase diagrams, the only three stable configurations are: ferromagnetic (FM), anti-ferromagnetic (AF) and super anti-ferromagnetic (SAF). We predicted also the frustrated phases when (J 2 /J 1 = −0.5 and J 2 /J 1 = +0.5), this ratio coupling depending on the interaction coupling between the 1st and 2nd nearest neighbors. For low temperature values, the total and partial magnetizations are found to be in good agreement with those found in the ground state phase diagrams. To complete this study, we present and discuss the frustrated phases in the both cases: the ferromagnetic and anti-ferromagnetic states.