The phase diagram of the next-neighbour Ising model of the face-centred cubic lattice

We use Monte Carlo simulation to determine the stable structures in the second-neighbour Ising model on the face-centred cubic lattice. Those structures are $\text{L1}_1$ for strongly antiferromagnetic second-neighbour interactions and $\text{L1}_0$ for ferromagnetic and weakly antiferromagnetic second neighbours. We find a third stable “intermediate” antiferromagnetic phase with $\text{I4}_1/amd$ symmetry, and calculate the paramagnetic transition temperature for each. The transition temperature depends strongly on second-neighbour interactions which are not frustrated. We determine a sublattice structure suitable for solving this problem with mean-field theory