  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 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 the specific heat critical exponent $\alpha$. Along with the space
dimension D, it appears to depend on the ratio of strength of the short-range
and long-range interactions.
