Monte Carlo study of the classical antiferromagnetic $J_1$-$J_2$-$J_3$ Heisenberg model on a simple cubic lattice
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915816555937792 |
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| author | Ignatenko, A. N. Streltsov, S. V. Irkhin, V. Yu. |
| author_facet | Ignatenko, A. N. Streltsov, S. V. Irkhin, V. Yu. |
| contents | An extensive Monte Carlo study of the classical Heisenberg model on a simple cubic lattice with antiferromagnetic exchange interactions $J_n$ between the first, second, and third neighbors is performed in a broad region of $J_2 / J_1$, $J_3 / J_1$ ratios, and temperature. The character of the phase transitions is analyzed via the Binder cumulant method. The Neel temperature $T_{\mathrm{N}}$ and the frustration parameter (the ratio $f= |θ|/T_{\mathrm{N}}$, $θ$ being the Curie-Weiss temperature) are calculated. A comparison with the Tyablikov approximation is carried out. The strength of the frustration effects is explored. Possible applications to antiferromagnetic perovskites, such as CaMnO$_3$ and HgMnO$_3$, are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16471 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monte Carlo study of the classical antiferromagnetic $J_1$-$J_2$-$J_3$ Heisenberg model on a simple cubic lattice Ignatenko, A. N. Streltsov, S. V. Irkhin, V. Yu. Strongly Correlated Electrons An extensive Monte Carlo study of the classical Heisenberg model on a simple cubic lattice with antiferromagnetic exchange interactions $J_n$ between the first, second, and third neighbors is performed in a broad region of $J_2 / J_1$, $J_3 / J_1$ ratios, and temperature. The character of the phase transitions is analyzed via the Binder cumulant method. The Neel temperature $T_{\mathrm{N}}$ and the frustration parameter (the ratio $f= |θ|/T_{\mathrm{N}}$, $θ$ being the Curie-Weiss temperature) are calculated. A comparison with the Tyablikov approximation is carried out. The strength of the frustration effects is explored. Possible applications to antiferromagnetic perovskites, such as CaMnO$_3$ and HgMnO$_3$, are discussed. |
| title | Monte Carlo study of the classical antiferromagnetic $J_1$-$J_2$-$J_3$ Heisenberg model on a simple cubic lattice |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2602.16471 |