When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909155945611264 |
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| author | Honchar, Yu. Berche, B. Holovatch, Yu. Kenna, R. |
| author_facet | Honchar, Yu. Berche, B. Holovatch, Yu. Kenna, R. |
| contents | We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation length is not bound by the system's physical size, a belief that long held sway. Instead, two scaling regimes can be observed - at the critical and pseudo-critical temperatures. We demonstrate that both are manifest for free boundaries. We use numerical simulations of the $d=5$ Ising model to analyse the magnetization, susceptibility, magnetization Fourier modes and the partition function zeros. While some of the response functions hide the dual finite-size scaling, the precision enabled by the analysis of Lee-Yang zeros allows this be brought to the fore. In particular, finite-size scaling of leading zeros at the pseudo-critical point confirms recent predictions coming from correlations exceeding the system size. This paper is dedicated to Jaroslav Ilnytskyi on the occasion of his 60th birthday. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_11721 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension Honchar, Yu. Berche, B. Holovatch, Yu. Kenna, R. Statistical Mechanics We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation length is not bound by the system's physical size, a belief that long held sway. Instead, two scaling regimes can be observed - at the critical and pseudo-critical temperatures. We demonstrate that both are manifest for free boundaries. We use numerical simulations of the $d=5$ Ising model to analyse the magnetization, susceptibility, magnetization Fourier modes and the partition function zeros. While some of the response functions hide the dual finite-size scaling, the precision enabled by the analysis of Lee-Yang zeros allows this be brought to the fore. In particular, finite-size scaling of leading zeros at the pseudo-critical point confirms recent predictions coming from correlations exceeding the system size. This paper is dedicated to Jaroslav Ilnytskyi on the occasion of his 60th birthday. |
| title | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2311.11721 |