  We have performed multicanonical simulations to study the critical behavior
of the two-dimensional Ising model with dipole interactions. This study
concerns the thermodynamic phase transitions in the range of the interaction
\delta where the phase characterized by striped configurations of width h=1 is
observed. Controversial results obtained from local update algorithms have been
reported for this region, including the claimed existence of a second-order
phase transition line that becomes first order above a tricritical point
located somewhere between \delta=0.85 and 1. Our analysis relies on the complex
partition function zeros obtained with high statistics from multicanonical
simulations. Finite size scaling relations for the leading partition function
zeros yield critical exponents \nu that are clearly consistent with a single
second-order phase transition line, thus excluding such tricritical point in
that region of the phase diagram. This conclusion is further supported by
analysis of the specific heat and susceptibility of the orientational order
parameter.
