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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2506.22296 |
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| _version_ | 1866911026576883712 |
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| author | Kastner, Michael |
| author_facet | Kastner, Michael |
| contents | Systems with long-range interactions have seen a surge of interest in the past decades. In the wake of this surge, the use of a system size dependent rescaling, sometimes termed "Kac prescription," of the long-range pair potential has seen widespread use. This ad hoc modification of the Hamiltonian makes the energy extensive, but its physical justification and implications are a frequent source of confusion and misinterpretation. After all, in real physical $N$-body systems, the pair interaction strength does not scale with the number $N$ of constituents. This article presents, at an introductory level, scaling arguments that provide a clear physical interpretation of the "Kac prescription" for finite systems as well as in the thermodynamic limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-range systems, (non)extensivity, and the rescaling of energies Kastner, Michael Statistical Mechanics Systems with long-range interactions have seen a surge of interest in the past decades. In the wake of this surge, the use of a system size dependent rescaling, sometimes termed "Kac prescription," of the long-range pair potential has seen widespread use. This ad hoc modification of the Hamiltonian makes the energy extensive, but its physical justification and implications are a frequent source of confusion and misinterpretation. After all, in real physical $N$-body systems, the pair interaction strength does not scale with the number $N$ of constituents. This article presents, at an introductory level, scaling arguments that provide a clear physical interpretation of the "Kac prescription" for finite systems as well as in the thermodynamic limit. |
| title | Long-range systems, (non)extensivity, and the rescaling of energies |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2506.22296 |