Phase diagram of the two-dimensional Ising model with dipolar interaction

We treat the two-dimensional Ising model with the dipolar interaction by the numerical calculation under the restriction that the spin configurations are distributed with a 4 x 4 period. The phase diagram with respect to temperature and dipolar interaction strength is constructed. Most characters of the phase diagram are consistent with those obtained in the references by the Monte Carlo simulation, except that we find a new rectangle phase, which is ordered in the spin structure with the 1 x 2 rectangle.