Monte Carlo study on Heisenberg model with local dipolar interaction
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915484931194880 |
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| author | Itou, Etsuko Matsumoto, Akira Nakayama, Yu Onagi, Toshiki |
| author_facet | Itou, Etsuko Matsumoto, Akira Nakayama, Yu Onagi, Toshiki |
| contents | Aharony and Fisher showed that non-local dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point, called the dipolar fixed point. The non-perturbative nature of the new fixed point, however, has not been uncovered for many decades. Inspired by the recent understanding that the dipolar fixed point is scale-invariant but not conformal invariant, we perform the Monte Carlo simulation of the local Heisenberg-dipolar model on the lattice of $40^3$ by introducing the local cost function parameterized by a parameter $λ$ and study its critical exponents, which should become identical to the dipolar fixed point of Aharony and Fisher in the infinite coupling limit $λ= \infty$. We find that the critical exponents become noticeably different from those of the Heisenberg fixed point for a finite coupling constant $λ=8$ (e.g. $ν=0.601(2)(^{+0}_{-2})$ in the local Heisenberg-dipolar model while $ν=0.712(1)(^{+3}_{-0})$ in the Heisenberg model), and the spin correlation function has a feature that it becomes divergence-free, implying the lack of conformal invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monte Carlo study on Heisenberg model with local dipolar interaction Itou, Etsuko Matsumoto, Akira Nakayama, Yu Onagi, Toshiki High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Lattice Aharony and Fisher showed that non-local dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point, called the dipolar fixed point. The non-perturbative nature of the new fixed point, however, has not been uncovered for many decades. Inspired by the recent understanding that the dipolar fixed point is scale-invariant but not conformal invariant, we perform the Monte Carlo simulation of the local Heisenberg-dipolar model on the lattice of $40^3$ by introducing the local cost function parameterized by a parameter $λ$ and study its critical exponents, which should become identical to the dipolar fixed point of Aharony and Fisher in the infinite coupling limit $λ= \infty$. We find that the critical exponents become noticeably different from those of the Heisenberg fixed point for a finite coupling constant $λ=8$ (e.g. $ν=0.601(2)(^{+0}_{-2})$ in the local Heisenberg-dipolar model while $ν=0.712(1)(^{+3}_{-0})$ in the Heisenberg model), and the spin correlation function has a feature that it becomes divergence-free, implying the lack of conformal invariance. |
| title | Monte Carlo study on Heisenberg model with local dipolar interaction |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2503.15874 |