Universality and criticality of a secondorder granular solidliquidlike phase transition
Abstract
We experimentally study the critical properties of the nonequilibrium solidliquidlike transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the bondorientational order parameter Q_{4}, which measures the degree of local crystallization. Two setups are compared, which present the transition at different critical accelerations as a result of modifying the energy dissipation parameters. In both setups five independent critical exponents are measured, associated to different properties of Q_{4}: the correlation length, relaxation time, vanishing wavenumber limit (static susceptibility), the hydrodynamic regime of the pair correlation function, and the amplitude of the order parameter. The respective critical exponents agree in both setups and are given by ν_{⊥}=1 ,ν_{∥}=2 ,γ =1 ,η ≈0.6 0.67 , and β =1 /2 , whereas the dynamical critical exponent is z =ν_{∥}/ν_{⊥}=2 . The agreement on five exponents is an exigent test for the universality of the transition. Thus, while dissipation is strictly necessary to form the crystal, the path the system undergoes toward the phase separation is part of a welldefined universality class. In fact, the local order shows critical properties while density does not. Being the later conserved, the appropriate model that couples both is model C in the Hohenberg and Halperin classification. The measured exponents are in accord with the nonequilibrium extension to model C if we assume that α , the exponent associated in equilibrium to the specific heat divergence but with no counterpart in this nonequilibrium experiment, vanishes.
 Publication:

Physical Review E
 Pub Date:
 January 2015
 DOI:
 10.1103/PhysRevE.91.012141
 arXiv:
 arXiv:1501.05002
 Bibcode:
 2015PhRvE..91a2141C
 Keywords:

 64.60.Ht;
 64.70.qj;
 05.40.a;
 45.70.n;
 Dynamic critical phenomena;
 Dynamics and criticality;
 Fluctuation phenomena random processes noise and Brownian motion;
 Granular systems;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter;
 82C27;
 76T25
 EPrint:
 14 pages, 13 figures, accepted in PRE