Critical behavior of the 2D Ising model modulated by the Octonacci sequence

G. A. Alves, M. S. Vasconcelos, T. F. A. Alves

Published 2017-09-22Version 1

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 Edwards-Anderson order parameter ($q_{EA}$), the 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 on Edwards-Anderson order parameter with critical temperature around $T_{c} \approx 1.411$, and the critical exponents $\beta$, $\gamma$ and $\nu$. The values are close to the Fibonacci case and they both differ from the pure Ising case. Also remarkable is the fact of the Octonacci sequence induces a different ordering in a two-dimensional system.