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arXiv · 2303.07733

Higher-order tensor renormalization group study of the $J_1$-$J_2$ Ising model on a square lattice

Kota Yoshiyama·Koji Hukushima
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Abstract

Phase transitions of the $J_1$-$J_2$ Ising model on a square lattice are studied using the higher-order tensor renormalization group(HOTRG) method. This system involves a competition between the ferromagnetic interaction $J_1$ and antiferromagnetic interaction $J_2$. Furthermore, weak first-order and second-order transitions are observed near the ratio $g=J_2/|J_1|=1/2$. Our results (based on HOTRG calculations for significantly larger sizes) indicate that the region of the first-order transition is marginally narrower than that in previous studies. Moreover, the universality class of the second-order transition connected to the transition line is not necessarily fully consistent with the Ashkin--Teller class considered earlier.

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Kota Yoshiyama, Koji Hukushima. 2023-03-14. Higher-order tensor renormalization group study of the $J_1$-$J_2$ Ising model on a square lattice. https://arxiv.org/abs/2303.07733

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