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

TL;DR

This study uses finite-size Monte Carlo simulations to analyze the critical behavior of the Fibonacci-modulated Ising model on a triangular lattice, revealing logarithmic corrections consistent with the Ising universality class.

Contribution

It introduces a detailed numerical analysis of the Fibonacci-modulated Ising model, highlighting the presence of logarithmic corrections in its critical behavior.

Findings

Critical temperature around 1.4116

System obeys Ising universality class

Logarithmic corrections affect critical exponents

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.