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

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

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arXiv · 1805.05725

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

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

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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 ($χ$) 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 $β$, $γ$ and $ν$, and the correction exponents $\hatβ$, $\hatγ$, $\hatα$ and $\hatλ$. Our results show that the system obeys the Ising model universality class and that the critical behavior has logarithmic corrections.

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T. F. A. Alves, G. A. Alves, M. S. Vasconcelos. 2018-05-15. Logarithm corrections in the critical behavior of the Ising model on a triangular lattice modulated with the Fibonacci sequence. https://arxiv.org/abs/1805.05725

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