Specific heat and structure factor in the square ANNNI model by Monte Carlo simulation

The axial (or anisotropic) next-nearest-neighbor Ising (ANNNI) model has been widely investigated: exact solution exists in one dimension; analytic and numerical treatments in two, and three dimensions suggest a rich phase diagram. Some controversial results obtained especially by Monte Carlo (MC) simulations are discussed. We conclude that in the region of weak competition (kappa=-J(2)/J(1) < 1/2) the size scaling analysis is the same as that obtained in the nearest-neighbor (NN) Ising model. For kappa > 1/2 we find a series of very sharp peaks in the specific heat due to the discreteness of the lattice. The structure factor supports and explains the existence of the specific heat peaks. Very long simulations have been performed (10^7 and 10^8 MC steps per spin) because the relaxation time is huge for such a frustrated system. A careful comparison of MC simulations for different lattice sizes suggests that the Kosterlitz-Thouless phase is present for all kappa > 1/2.