  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 L1_1 for strongly antiferromagnetic second neighbour
interactions and L1_0 for ferromagnetic and weakly antiferromagnetic second
neighbours. We find a third stable "intermediate" antiferromagnetic phase with
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. Our results contradict a recent paper, which also
reported two different AFM structures and a new "intermediate" phase exists in
this system. Here we show that the assumed sublattice structure in is
inconsistent with the ground state. We determine a sublattice structure
suitable for solving this problem with mean field theory.
