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

TL;DR

This study explores the critical behavior of a 2D Ising model with interactions modulated by the quasiperiodic Octonacci sequence, revealing a continuous phase transition with Ising universality and logarithmic corrections.

Contribution

It introduces the analysis of the 2D Ising model with Octonacci sequence modulation, applying Monte Carlo simulations and finite size scaling to determine critical properties.

Findings

Critical temperature around 1.413

Obeys Ising universality class with logarithmic corrections

Estimated correction exponents for finite size scaling

Abstract

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.