The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917077027127296 |
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| author | Yao, Dingyun Xiao, Tianning Zhang, Chao Deng, Youjin Fan, Zhijie |
| author_facet | Yao, Dingyun Xiao, Tianning Zhang, Chao Deng, Youjin Fan, Zhijie |
| contents | The two-dimensional (2D) XY model plays a crucial role in statistical and condensed matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between non-classical and short-range universality classes.In this work, we investigate the 2D XY model with algebraically decaying interactions $\sim 1/r^{2+σ}$, and provide a comprehensive numerical analysis of its thermodynamic properties. We demonstrate that for $σ\leq 2$, the system undergoes a second-order phase transition into a ferromagnetic phase characterized by the emergence of long-range order. In the low-temperature phase, due to the presence of the Goldstone mode, the correlation function saturates to a non-zero constant in the form of a power law for $σ< 2$, with decaying exponent $2-σ$, and in the form of the inverse logarithm of distance for $σ=2$. Moreover, the critical points and exponents are also determined for various $σ$. We provide compelling evidence that the crossover between non-classical and short-range regimes occurs at $σ=2$. This work presents a detailed account of the simulation methodology, extensive numerical data, and new insights into the physics of long-range interacting systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_01811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study Yao, Dingyun Xiao, Tianning Zhang, Chao Deng, Youjin Fan, Zhijie Statistical Mechanics The two-dimensional (2D) XY model plays a crucial role in statistical and condensed matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between non-classical and short-range universality classes.In this work, we investigate the 2D XY model with algebraically decaying interactions $\sim 1/r^{2+σ}$, and provide a comprehensive numerical analysis of its thermodynamic properties. We demonstrate that for $σ\leq 2$, the system undergoes a second-order phase transition into a ferromagnetic phase characterized by the emergence of long-range order. In the low-temperature phase, due to the presence of the Goldstone mode, the correlation function saturates to a non-zero constant in the form of a power law for $σ< 2$, with decaying exponent $2-σ$, and in the form of the inverse logarithm of distance for $σ=2$. Moreover, the critical points and exponents are also determined for various $σ$. We provide compelling evidence that the crossover between non-classical and short-range regimes occurs at $σ=2$. This work presents a detailed account of the simulation methodology, extensive numerical data, and new insights into the physics of long-range interacting systems. |
| title | The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2411.01811 |