Two-dimensional XY Ferromagnet Induced by Long-range Interaction
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912705511686144 |
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| author | Xiao, Tianning Yao, Dingyun Zhang, Chao Fan, Zhijie Deng, Youjin |
| author_facet | Xiao, Tianning Yao, Dingyun Zhang, Chao Fan, Zhijie Deng, Youjin |
| contents | The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of long-range interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction $\sim1/r^{2+σ}$. Utilizing an advanced update strategy, we conduct large-scale Monte Carlo simulations of the model up to a linear size of $L=8192$. Our results demonstrate continuous phase transitions into a ferromagnetic phase for $σ\leq 2$, which exhibits the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at $σ= 2$. The observed scaling behaviors in the low-temperature phase for $σ\le 2$ agree with our theoretical analysis. Our findings request further theoretical understandings and can be of practical application in cutting-edge experiments like Rydberg atom arrays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-dimensional XY Ferromagnet Induced by Long-range Interaction Xiao, Tianning Yao, Dingyun Zhang, Chao Fan, Zhijie Deng, Youjin Statistical Mechanics The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of long-range interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction $\sim1/r^{2+σ}$. Utilizing an advanced update strategy, we conduct large-scale Monte Carlo simulations of the model up to a linear size of $L=8192$. Our results demonstrate continuous phase transitions into a ferromagnetic phase for $σ\leq 2$, which exhibits the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at $σ= 2$. The observed scaling behaviors in the low-temperature phase for $σ\le 2$ agree with our theoretical analysis. Our findings request further theoretical understandings and can be of practical application in cutting-edge experiments like Rydberg atom arrays. |
| title | Two-dimensional XY Ferromagnet Induced by Long-range Interaction |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2404.08498 |