Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929522063966208 |
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| author | Ruiz-Lorenzo, J. J. |
| author_facet | Ruiz-Lorenzo, J. J. |
| contents | We have studied numerically the Lee-Yang singularities of the four dimensional Ising model at criticality, which is believed to be in the same universality class as the $ϕ_4^4$ scalar field theory. We have focused in the numerical characterization of the logarithmic corrections to the scaling of the zeros of the partition function and its cumulative probability distribution, finding a very good agreement with the predictions of the renormalization group computation on the $ϕ_4^4$ scalar field theory. To obtain these results, we have extended a previous study [R. Kenna, C. B. Lang, Nucl. Phys., 1993, B393, 461] in which there were computed numerically the first two zeros for $L\leqslant 24$ lattices, to the computation of the first four zeros for $L\leqslant 64$ lattices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_03932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna Ruiz-Lorenzo, J. J. Statistical Mechanics Disordered Systems and Neural Networks We have studied numerically the Lee-Yang singularities of the four dimensional Ising model at criticality, which is believed to be in the same universality class as the $ϕ_4^4$ scalar field theory. We have focused in the numerical characterization of the logarithmic corrections to the scaling of the zeros of the partition function and its cumulative probability distribution, finding a very good agreement with the predictions of the renormalization group computation on the $ϕ_4^4$ scalar field theory. To obtain these results, we have extended a previous study [R. Kenna, C. B. Lang, Nucl. Phys., 1993, B393, 461] in which there were computed numerically the first two zeros for $L\leqslant 24$ lattices, to the computation of the first four zeros for $L\leqslant 64$ lattices. |
| title | Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2402.03932 |