  We investigated the Ising model on a square lattice with ferro and
antiferromagnetic interactions modulated by the quasiperiodic Octonacci
sequence in both directions of the lattice. We have applied the Replica
Exchange Monte Carlo (Parallel Tempering) technique to calculate the
thermodynamic quantities of the system. We obtained the order parameter, the
associated magnetic susceptibility ($\chi$) and the specific heat $(c)$ in
order to characterize the universality class of the phase transition. Also, we
use the finite size scaling method to obtain the critical temperature of the
system and the critical exponents $\beta$, $\gamma$ and $\nu$. In the low
temperature limit we have obtained a continuous transition with critical
temperature around $T_{c} \approx 1.413$. The system obeys the Ising
universality class with logarithmic corrections. We found estimatives for the
correction exponents $\hat{\beta}$, $\hat{\gamma}$ and $\hat{\lambda}$ by using
the finite size scaling technique.
