  We investigated the critical behavior of the Ising model in a triangular
lattice with ferro and anti-ferromagnetic interactions modulated by the
Fibonacci sequence, by using finite-size numerical simulations. Specifically,
we used a replica exchange Monte Carlo method, known as Parallel Tempering, to
calculate the thermodynamic quantities of the system. We have obtained the
staggered magnetization $q$, the associated magnetic susceptibility ($\chi$)
and the specific heat $c$, to characterize the universality class of the
system. At the low-temperature limit, we have obtained a continuous phase
transition with a critical temperature around $T_{c} \approx 1.4116$ for a
particular modulation of the lattice according to the Fibonacci letter
sequence. In addition, we have used finite-size scaling relations with
logarithmic corrections to estimate the critical exponents $\beta$, $\gamma$
and $\nu$, and the correction exponents $\hat{\beta}$, $\hat{\gamma}$,
$\hat{\alpha}$ and $\hat{\lambda}$. Our results show that the system obeys the
Ising model universality class and that the critical behavior has logarithmic
corrections.
