  The two-dimensional Ising model with nearest-neighbor ferromagnetic and
long-range dipolar interactions exhibits a rich phase diagram. The presence of
the dipolar interaction changes the ferromagnetic ground state expected for the
pure Ising model to a series of striped phases as a function of the interaction
strengths. Monte Carlo simulations and histogram reweighting techniques applied
to multiple histograms are performed to identify the critical temperatures for
the phase transitions taking place for stripes of width $h=2$ on square
lattices. In particular, we aim to study the intermediate nematic phase, which
is observed for large lattice sizes only. For these lattice sizes, we calculate
the critical temperatures for the striped-nematic and nematic-tetragonal
transitions, critical exponents, and the bulk free-energy barrier associated
with the coexisting phases. We also evaluate the long-term correlations in our
time series near the finite-size critical points by studying the integrated
autocorrelation time $\tau$ as a function of the lattice size. This allows us
to infer how severe the critical slowing down for this system with long-range
interaction and nearby thermodynamic phase transitions is.
