When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
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...
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| Format: | Article |
| Language: | English |
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Institute for Condensed Matter Physics
2024-03-01
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| Series: | Condensed Matter Physics |
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| Online Access: | https://cmpj2.icmp.lviv.ua/index.php/cmpj/article/view/37 |
| _version_ | 1797234945550188544 |
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| author | Yu. Honchar B. Berche Yu. Holovatch R. Kenna |
| author_facet | Yu. Honchar B. Berche Yu. Holovatch R. Kenna |
| author_sort | Yu. Honchar |
| collection | DOAJ |
| description |
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.
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| first_indexed | 2024-04-24T16:40:08Z |
| format | Article |
| id | doaj.art-f28d3dc3ac004868afc71e11e32a4b60 |
| institution | Directory Open Access Journal |
| issn | 1607-324X 2224-9079 |
| language | English |
| last_indexed | 2024-04-24T16:40:08Z |
| publishDate | 2024-03-01 |
| publisher | Institute for Condensed Matter Physics |
| record_format | Article |
| series | Condensed Matter Physics |
| spelling | doaj.art-f28d3dc3ac004868afc71e11e32a4b602024-03-29T10:14:53ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2224-90792024-03-0127110.5488/cmp.27.13603When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimensionYu. Honchar0https://orcid.org/0000-0003-2660-4593B. Berche1https://orcid.org/0000-0002-4254-807XYu. Holovatch2https://orcid.org/0000-0002-1125-2532R. Kenna3https://orcid.org/0000-0001-9990-4277Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Centre for Fluids and Complex Systems, Coventry University, Coventry CV1 5FB, UK; L4 Collaboration and Doctoral College for the Statistical Physics of Complex Systems, Lviv-Leipzig-Lorraine-Coventry, EuropeLaboratoire de Physique et Chimie Théoriques, Université de Lorraine - CNRS, Nancy Cedex, France; L4 Collaboration and Doctoral College for the Statistical Physics of Complex Systems, Lviv-Leipzig-Lorraine-Coventry, Europe; Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Centre for Fluids and Complex Systems, Coventry University, Coventry CV1 5FB, UK; L4 Collaboration and Doctoral College for the Statistical Physics of Complex Systems, Lviv-Leipzig-Lorraine-Coventry, Europe; Complexity Science Hub Vienna, 1080 Vienna, AustriaCentre for Fluids and Complex Systems, Coventry University, Coventry CV1 5FB, UK; L4 Collaboration and Doctoral College for the Statistical Physics of Complex Systems, Lviv-Leipzig-Lorraine-Coventry, Europe 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. https://cmpj2.icmp.lviv.ua/index.php/cmpj/article/view/37universalityfinite-size scalingupper critical dimension |
| spellingShingle | Yu. Honchar B. Berche Yu. Holovatch R. Kenna When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension Condensed Matter Physics universality finite-size scaling upper critical dimension |
| title | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension |
| title_full | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension |
| title_fullStr | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension |
| title_full_unstemmed | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension |
| title_short | When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension |
| title_sort | when correlations exceed system size finite size scaling in free boundary conditions above the upper critical dimension |
| topic | universality finite-size scaling upper critical dimension |
| url | https://cmpj2.icmp.lviv.ua/index.php/cmpj/article/view/37 |
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