The XXZ instantiation of the Heisenberg model, a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems in which the spins of the magnetic systems are treated quantum mechanically.
The generalized $XXZ$ model is given by the Hamiltonian:
$$H = \sum_{\langle i,j \rangle}S^x_iS^x_j+S^y_iS^y_j+\Delta S^z_iS^z_j,$$
where $\Delta = -1$ represents the case of the ferromagnet and $\Delta = 1$ characterizes that of the antiferromagnet.
