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Scaling collapse at the jamming transition.

¹Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501.

Physical Review. E

|February 13, 2016

Summary

This summary is machine-generated.

This study numerically investigates a simple jamming model, finding critical exponents matching sphere jamming. Results support the model

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Area of Science:

Physics
Statistical Mechanics
Computational Physics

Background:

The jamming transition in disordered systems is a critical phenomenon.
It is characterized by properties like power-law distributions of marginal contacts.

Purpose of the Study:

To numerically investigate a simple jamming model with finite-range interactions.
To test the conjecture that this model belongs to the same universality class as sphere jamming.
To extract precise critical exponents and analyze finite-size scaling effects.

Main Methods:

Numerical simulations of a recently proposed simple jamming model.
Extraction of critical exponents (θ and γ).
Analysis of finite-size scaling effects in subcritical regimes.

Main Results:

Numerical estimates for critical exponents θ=0.451±0.006 and γ=0.404±0.004 were obtained.
These exponents align with those observed in sphere packing systems.
Finite-size scaling analysis revealed subcritical cutoff regimes and protocol-dependent curves.

Conclusions:

The findings support the conjectured universality class link between the studied model and sphere jamming.
More precise critical exponent measurements were provided compared to previous studies.
New insights into the finite-size scaling behavior of continuous constraint satisfaction transitions were gained.