On the phase diagram of the 2d ising model with frustrating dipole interaction

Due to intrinsic frustrations of interaction, the 2d Ising model with competing ferromagnetic short-range nearest-neighbour and antiferromagnetic long-range dipole interactions possesses a rich phase diagram. The order of the phase transition from the striped h = 1 phase to the tetragonal phase that is observed in this model has been a subject of recent controversy. We address this question by using the partition function density analysis in the complex temperature plane. Our results support the second-order phase transition scenario. To measure the strength of the phase transition, we calculate the values of specific heat critical exponent α. Along with the space dimension, it appears to depend on the ratio of strengths of the short-range and long-range interactions.