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We use Monte Carlo simulation to determine the stable structures in thesecond-neighbour Ising model on the face-centred cubic lattice. Thosestructures are L1_1 for strongly antiferromagnetic second neighbourinteractions and L1_0 for ferromagnetic and weakly antiferromagnetic secondneighbours. We find a third stable "intermediate" antiferromagnetic phase withI4_1/amd symmetry, and calculate the paramagnetic transition temperature foreach.  The transition temperature depends strongly on second neighbour interactionswhich are not frustrated. Our results contradict a recent paper, which alsoreported two different AFM structures and a new "intermediate" phase exists inthis system. Here we show that the assumed sublattice structure in isinconsistent with the ground state. We determine a sublattice structuresuitable for solving this problem with mean field theory.

On the existence of an intermediate phase in the antiferromagnetic Ising model on an face-centered cubic lattice