Two dimensional compass model with Heisenberg interactions

Highlights: • The compass model with next and next near neighbor interactions is studied. • The phase diagram at zero temperature is presented. • The critical temperature for some values of the parameters is calculated. We consider a two dimensional compass model with a next and a next near Heisenberg term. The interactions are of two types: frustrated near neighbor compass interactions of amplitudes J_x and J_y, and next and next near neighbor Heisenberg interactions with exchanges J₁ and J₂ respectively. The Heisenberg interactions are isotropic in spin space, but the compass interactions depend on the bond direction. The ground state of the pure compass model is degenerated with a complex phase diagram. This degeneracy is removed by the Heisenberg terms leading to the arising of a magnetically ordered phase with a preferred direction. We calculate the phase diagrams at zero temperature for the case where, for J₂ = 0, we have an antiferromagnetic ground state. We show that varying the value of J₂, a magnetically disordered phase can be reached for small values of the compass interactions. We also calculate the critical temperature for a specified value of parameters.