Universal and non-universal signatures in the scaling functions of critical variables
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910898606571520 |
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| author | Teza, Gianluca Stella, Attilio L. |
| author_facet | Teza, Gianluca Stella, Attilio L. |
| contents | The view that the probability density function (PDF) of a key statistical variable, anomalously scaled by size or time, could furnish a hallmark of universal behavior contrasts with the circumstance that such density sensibly depends on non-universal features. We solve this apparent contradiction by demonstrating that both non-universal amplitudes and universal exponents of leading critical singularities in large deviation functions are determined by the PDF tails, whose form is argued on extensivity. This unexplored scenario implies a universal form of central limit theorem at criticality and is confirmed by exact calculations for mean field Ising models in equilibrium and for anomalous diffusion models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal and non-universal signatures in the scaling functions of critical variables Teza, Gianluca Stella, Attilio L. Statistical Mechanics The view that the probability density function (PDF) of a key statistical variable, anomalously scaled by size or time, could furnish a hallmark of universal behavior contrasts with the circumstance that such density sensibly depends on non-universal features. We solve this apparent contradiction by demonstrating that both non-universal amplitudes and universal exponents of leading critical singularities in large deviation functions are determined by the PDF tails, whose form is argued on extensivity. This unexplored scenario implies a universal form of central limit theorem at criticality and is confirmed by exact calculations for mean field Ising models in equilibrium and for anomalous diffusion models. |
| title | Universal and non-universal signatures in the scaling functions of critical variables |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2407.07782 |