Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914283723423744 |
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| author | Dias, Pietro F. Zimmer, Fabio M. Fytas, Nikolaos G. Schmidt, Mateus |
| author_facet | Dias, Pietro F. Zimmer, Fabio M. Fytas, Nikolaos G. Schmidt, Mateus |
| contents | We investigate the frustrated $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice, featuring first- and second-neighbor ferromagnetic couplings ($J_1>0$ and $J_2>0$) and third-neighbor antiferromagnetic interactions ($J_3<0$). Using the cluster mean-field method, we analyze the phase transitions in the regime $1/2 < J_2/J_1 \le 1$, where ferromagnetic and antiferromagnetic phases compete. Our results reveal that near the strongly frustrated limit $J_3/J_1 = -1$, the system exhibits order-by-disorder state selection, tricritical and bicritical behavior, critical endpoints, and two successive phase transitions. The ferromagnetic-paramagnetic transition remains second order across the entire interaction range, whereas the antiferromagnetic-paramagnetic boundary shows a richer behavior, including both first- and second-order transitions as well as tricriticality. Increasing the second-neighbor coupling $J_2/J_1$ narrows the range of $J_3/J_1$ where first-order antiferromagnetic-paramagnetic transitions occur; beyond a certain threshold, only second-order order-disorder transitions persist. Consequently, the tricritical point shifts toward $J_3/J_1 \approx -1$ as $J_2/J_1$ increases, culminating in a bicritical point where the antiferromagnetic, ferromagnetic, and paramagnetic phases meet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19648 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice Dias, Pietro F. Zimmer, Fabio M. Fytas, Nikolaos G. Schmidt, Mateus Statistical Mechanics Strongly Correlated Electrons We investigate the frustrated $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice, featuring first- and second-neighbor ferromagnetic couplings ($J_1>0$ and $J_2>0$) and third-neighbor antiferromagnetic interactions ($J_3<0$). Using the cluster mean-field method, we analyze the phase transitions in the regime $1/2 < J_2/J_1 \le 1$, where ferromagnetic and antiferromagnetic phases compete. Our results reveal that near the strongly frustrated limit $J_3/J_1 = -1$, the system exhibits order-by-disorder state selection, tricritical and bicritical behavior, critical endpoints, and two successive phase transitions. The ferromagnetic-paramagnetic transition remains second order across the entire interaction range, whereas the antiferromagnetic-paramagnetic boundary shows a richer behavior, including both first- and second-order transitions as well as tricriticality. Increasing the second-neighbor coupling $J_2/J_1$ narrows the range of $J_3/J_1$ where first-order antiferromagnetic-paramagnetic transitions occur; beyond a certain threshold, only second-order order-disorder transitions persist. Consequently, the tricritical point shifts toward $J_3/J_1 \approx -1$ as $J_2/J_1$ increases, culminating in a bicritical point where the antiferromagnetic, ferromagnetic, and paramagnetic phases meet. |
| title | Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice |
| topic | Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2601.19648 |