Scaling collapse at the jamming transition

Abstract

The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of jamming, which is conjectured to lie in the same universality class as the jamming of spheres in all dimensions. We extract numerical estimates of the critical exponents, θ = 0.451 $\pm$ 0.006 and γ = 0.404 $\pm$ 0.004, that match the exponents observed in sphere packing systems. We analyze finite-size scaling effects that manifest in a subcritical cutoff regime and size-independent, but protocol-dependent scaling curves. Our results supports the conjectured link with sphere jamming, provide more precise measurements of the critical exponents than previously reported, and shed light on the finite-size scaling behavior of continuous constraint satisfiability transitions.

5 pages, 4 figures

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• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
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Cited by in corpus (7)

• Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems
• Experimental observations of marginal criticality in granular materials
• Finite size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder
• An exploratory study of the glassy landscape near jamming
• Jamming Criticality of Near-Crystals
• Introduction to the dynamics of disordered systems: equilibrium and gradient descent
• Infinitesimal asphericity changes the universality of the jamming transition