Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909938545065984 |
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| author | Yao, Dingyun Xiao, Tianning Fan, Zhijie Deng, Youjin |
| author_facet | Yao, Dingyun Xiao, Tianning Fan, Zhijie Deng, Youjin |
| contents | The introduction of decaying long-range (LR) interactions $1/r^{d+σ}$ has drawn persistent interest in understanding how system properties evolve with $σ$. The Sak's criterion and the extended Mermin-Wagner theorem have gained broad acceptance in predicting the critical and low-temperature (low-T) behaviors of such systems. We perform large-scale Monte Carlo simulations for the LR-Heisenberg model in two dimensions (2D) up to linear size $L=8192$, and show that, as long as for $σ\leq 2$, the system exhibits spontaneous symmetry breaking, via a single continuous phase transition, and develops a generic long-range order. We then introduce an LR simple random walk (LR-SRW) with the total walk length fixed at O($L^d$), satisfying the extensivity of statistical systems, and observe that the LR-SRW can faithfully characterize the low-T scaling behaviors of the LR-Heisenberg model in both 2D and 3D, as induced by Goldstone-mode fluctuations. Finally, based on insights from LR-SRW, we propose a general criterion for the phase transition and the low-T properties of LR statistical systems with continuous symmetry in any spatial dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model Yao, Dingyun Xiao, Tianning Fan, Zhijie Deng, Youjin Statistical Mechanics The introduction of decaying long-range (LR) interactions $1/r^{d+σ}$ has drawn persistent interest in understanding how system properties evolve with $σ$. The Sak's criterion and the extended Mermin-Wagner theorem have gained broad acceptance in predicting the critical and low-temperature (low-T) behaviors of such systems. We perform large-scale Monte Carlo simulations for the LR-Heisenberg model in two dimensions (2D) up to linear size $L=8192$, and show that, as long as for $σ\leq 2$, the system exhibits spontaneous symmetry breaking, via a single continuous phase transition, and develops a generic long-range order. We then introduce an LR simple random walk (LR-SRW) with the total walk length fixed at O($L^d$), satisfying the extensivity of statistical systems, and observe that the LR-SRW can faithfully characterize the low-T scaling behaviors of the LR-Heisenberg model in both 2D and 3D, as induced by Goldstone-mode fluctuations. Finally, based on insights from LR-SRW, we propose a general criterion for the phase transition and the low-T properties of LR statistical systems with continuous symmetry in any spatial dimension. |
| title | Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.01956 |