Finite size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder
| Autor: | R. Cameron Dennis, Eric I. Corwin, Rafael Díaz Hernández Rojas, Giorgio Parisi, Federico Ricci-Tersenghi, Patrick Charbonneau, Harukuni Ikeda |
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| Rok vydání: | 2020 |
| Předmět: |
Physics
Statistical Mechanics (cond-mat.stat-mech) jamming finite size scaling universality Dimension (graph theory) FOS: Physical sciences Jamming Disordered Systems and Neural Networks (cond-mat.dis-nn) Renormalization group Condensed Matter - Disordered Systems and Neural Networks Condensed Matter - Soft Condensed Matter finite size scaling 01 natural sciences Power law 010305 fluids & plasmas Stability conditions Distribution (mathematics) 0103 physical sciences Soft Condensed Matter (cond-mat.soft) universality Limit (mathematics) Statistical physics 010306 general physics jamming Scaling Condensed Matter - Statistical Mechanics |
| DOI: | 10.48550/arxiv.2011.10899 |
| Popis: | Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is that small interparticle forces ($f$) and gaps ($h$) are distributed according to nontrivial power laws. A recently developed mean-field (MF) theory predicts the characteristic exponents of these distributions in the limit of very high spatial dimension, $d\rightarrow\infty$ and, remarkably, their values seemingly agree with numerical estimates in physically relevant dimensions, $d=2$ and $3$. These exponents are further connected through a pair of inequalities derived from stability conditions, and both theoretical predictions and previous numerical investigations suggest that these inequalities are saturated. Systems at the jamming point are thus only marginally stable. Despite the key physical role played by these exponents, their systematic evaluation has yet to be attempted. Here, we carefully test their value by analyzing the finite-size scaling of the distributions of $f$ and $h$ for various particle-based models for jamming. Both dimension and the direction of approach to the jamming point are also considered. We show that, in all models, finite-size effects are much more pronounced in the distribution of $h$ than in that of $f$. We thus conclude that gaps are correlated over considerably longer scales than forces. Additionally, remarkable agreement with MF predictions is obtained in all but one model, namely near-crystalline packings. Our results thus help to better delineate the domain of the jamming universality class. We furthermore uncover a secondary linear regime in the distribution tails of both $f$ and $h$. This surprisingly robust feature is understood to follow from the (near) isostaticity of our configurations. Comment: Version accepted for publication |
| Databáze: | OpenAIRE |
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