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