Logarithm corrections in the critical behavior of the Ising model on a triangular lattice modulated with the Fibonacci sequence

Abstract: 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.