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Universality and criticality of a second-order granular solid-liquid-like phase transition
Gustavo Castillo1, Nicolás Mujica2, Rodrigo Soto2
1Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile and Laboratoire de Physique Statistique, Ecole Normale Supérieure, UMR CNRS 8550, 24 Rue Lhomond, 75005 Paris, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 14, 2015
Summary
We studied the nonequilibrium solid-liquid transition in vibrated granular matter. Critical exponents for local crystallization agree across setups, confirming universality despite varying dissipation.
Area of Science:
- Physics of granular materials
- Non-equilibrium statistical mechanics
- Phase transitions
Background:
- Granular matter exhibits complex behaviors, including solid-liquid-like transitions under vibration.
- Understanding critical properties and universality classes in non-equilibrium systems is crucial.
- The role of energy dissipation in driving phase transitions needs further investigation.
Purpose of the Study:
- To experimentally investigate the critical properties of the nonequilibrium solid-liquid-like transition in vibrated granular matter.
- To characterize the critical dynamics by coupling the density field with the bond-orientational order parameter Q(4).
- To test the universality of this transition by comparing critical exponents across different energy dissipation parameters.
Main Methods:
- Utilized two experimental setups with modified energy dissipation parameters to induce transitions at different critical accelerations.
- Measured five independent critical exponents associated with the order parameter Q(4): correlation length, relaxation time, static susceptibility, pair correlation function, and order parameter amplitude.
- Determined the dynamical critical exponent z.
Main Results:
- Identified critical dynamics characterized by the coupling of density and the local crystallization order parameter Q(4).
- Measured critical exponents ν(⊥)=1, ν(∥)=2, γ=1, η≈0.6-0.67, β=1/2, and z=2, which agreed between the two setups.
- Observed that local order exhibits critical properties, while density does not.
Conclusions:
- The agreement of five critical exponents strongly supports the universality of the nonequilibrium solid-liquid-like transition in vibrated granular matter.
- Dissipation is essential for crystal formation, but the phase separation pathway belongs to a defined universality class.
- The system's behavior aligns with a nonequilibrium extension of Model C, assuming vanishing specific heat exponent α.
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