Phase diagram of a square Ising model with exchange and dipole interactions: Monte Carlo simulations

The thermal behavior of the square Ising model with exchange (J) and dipole (g) interactions is well understood for values of J/g far from the phase boundaries between striped configurations of different widths h. A variety of phase transitions were found by Monte Carlo simulations. Both first order and continuous phase transitions were found depending on the value of the ratio J/g, but no intermediate phase was found between the low temperature ordered striped phase and the high temperature paramagnetic one. Here, we investigate the regions of J/g near the boundaries between the striped phases of width h and h+1. We find that for h=2,3, an intermediate (modulated) phase occurs between the striped and paramagnetic phases. Of particular interest is the region around the boundary between the Néel phase and the striped phase with h=1 where an infinite sequence of <1,n> (<n,1>) configurations, never seen before, are found to become stable. They are characterized by horizontal (vertical) stripes made up of n identical antiferromagnetic rows (columns) alternated with n antiferromagnetic rows (columns) of spins reversed. The accumulation point of this sequence (n->infinity) corresponds to the striped phase with h=1 (columnar phase).