Fluctuations and Criticality of a Granular Solid-Liquid-like

Fluctuations and Criticality of a Granular Solid-Liquid-like
Phase Transition
G. Castillo ∗, N. Mujica∗ and R. Soto∗
We present an experimental study of density and order fluctuations in the vicinity
of the solid-liquid-like transition that occurs in a vibrated quasi-two-dimensional granular system. We show that density fluctuations, characterized through the structure
factor S(k), increase in size and intensity as the transition is approached, but they
do not change significantly at the transition itself. The dense, metastable clusters
also increase their local order in the vicinity of the transition. This is characterized
through the bond-orientational order parameter Q4 , which in Fourier space obeys
an Ornstein-Zernike behavior. Depending on filling density and vertical height, the
transition can be of first or second order type. In the latter case, the associated correlation length ξ4 , relaxation time τ4 and zero k limit of Q4 fluctuations (susceptibility)
obey diverging critical power laws, with saturations due to finite size effects. Their
respective critical exponents are ν⊥ = 1, ν|| = 2 and γ = 1, whereas the dynamical critical exponent z = ν|| /ν⊥ = 2. These results are consistent with model C of
dynamical critical phenomena, valid for a non-conservative field (order) coupled to a
conservative one (density).
∗ Departamento de Fı́sica, Facultad de Ciencias Fı́sicas y Matemáticas, Universidad de Chile,
Casilla 487-3, Santiago, Chile
(a)
1
10
1
4
/d
4
S (0)
10
0
10
0
10
−2
10
−1
10
0
10
Figure 1: (color online). Susceptibility S4 (0) (◦), normalized correlation length ξ4 /d () as
functions of ε ≡ (Γc − Γ)/Γc . Continuous lines show critical power law fits, with exponents
γ = ν⊥ = 1 for S4 (0) and ξ4 .