The phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice
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arXiv
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2025
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| author | Li, Shang-Wei Tseng, Yuan-Heng Jiang, Fu-Jiun |
| author_facet | Li, Shang-Wei Tseng, Yuan-Heng Jiang, Fu-Jiun |
| contents | We study the phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice using the non-perturbative first principle Monte Carlo simulations. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest couplings, respectively. In particular, the values of $J_2/|J_1| = 0.20, 0.22, 0.23, 0.24, 0.3, 0.5, 0.8,$ and 1.0 are considered in our study. Based on the numerical outcomes, we find that the phase transitions for $J_2/|J_1| = 0.20, 0.22, 0.23,$ and 0.24 are second order and are governed by the 2D Ising universality class. In addition, we find evidence to support the facts that there are transitions for $J_2/|J_1| = 0.5, 0.8$ and 1.0 and these phase transitions are second order. Our results also indicate phase transition is unlikely to take place for $g=0.3$. We are not able to obtain results for $J_2/|J_1|$ $\in$ (0.24, 0.3) because the associated integrated autocorrelation times or (and) the equilibrium times are extremely large at the low-temperature region. A comparison between the outcomes presented here and the available results in the literature is briefly conducted as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_11437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice Li, Shang-Wei Tseng, Yuan-Heng Jiang, Fu-Jiun High Energy Physics - Lattice Statistical Mechanics We study the phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice using the non-perturbative first principle Monte Carlo simulations. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest couplings, respectively. In particular, the values of $J_2/|J_1| = 0.20, 0.22, 0.23, 0.24, 0.3, 0.5, 0.8,$ and 1.0 are considered in our study. Based on the numerical outcomes, we find that the phase transitions for $J_2/|J_1| = 0.20, 0.22, 0.23,$ and 0.24 are second order and are governed by the 2D Ising universality class. In addition, we find evidence to support the facts that there are transitions for $J_2/|J_1| = 0.5, 0.8$ and 1.0 and these phase transitions are second order. Our results also indicate phase transition is unlikely to take place for $g=0.3$. We are not able to obtain results for $J_2/|J_1|$ $\in$ (0.24, 0.3) because the associated integrated autocorrelation times or (and) the equilibrium times are extremely large at the low-temperature region. A comparison between the outcomes presented here and the available results in the literature is briefly conducted as well. |
| title | The phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice |
| topic | High Energy Physics - Lattice Statistical Mechanics |
| url | https://arxiv.org/abs/2509.11437 |