Phases and Phase Transitions of an Anisotropic Ising-O(3) Model

The two-dimensional anisotropic Ising-O(3) model is an effective Hamiltonian for the
square-lattice J1-J2 Heisenberg model, with nearest-neighbor coupling J1 along with
frustrated and dominant next-nearest-neighbor coupling J2. We employ Monte Carlo
simulation of the Ising-O(3) model to determine its phase diagram as a function of the
anisotropy of the O(3) spins and the temperature. For sufficiently large anisotropy, there is a
direct transition from the paramagnetic high-temperature phase to the low-temperature phase
that breaks both spin and nematic (Ising) symmetries. This transition splits into two separate
transitions as the anisotropy is lowered, leading to the appearance of an Ising-ordered
intermediate phase. We also determine the orders of the phase transitions. These results can
be related to the experimental observations of the orders and sequences of magnetic and
structural transitions in quasi-2D ferropnictide materials.