Scale Separation of Shear-Induced Criticality in Glasses

In a sheared steady state, glasses reach a nonequilibrium criticality called yielding criticality. We report that the qualitative nature of this nonequilibrium critical phenomenon depends on the details of the system and that responses and fluctuations are governed by different critical correlation lengths in specific situations. This scale separation of critical lengths arises when the screening of elastic propagation of mechanical signals is not negligible. We also discuss the determinant of the impact of screening effects from the viewpoint of the microscopic dissipation mechanism.

Figure 1

Strain-based diffusion constant $\widehat{D}$ as a function of $\dot{\gamma }$. Results for (a) system A and (b) system B.

Figure 2

(a),(b) Average number density of STs $⟨n_{\mathrm{ST}}⟩$ as a function of the shear rate $\dot{\gamma }$. The dashed lines are the fitting results using all data points and have slopes of $1/{\beta }_{\mathrm{A}}\approx 0.72$ and $1/{\beta }_{\mathrm{B}}\approx 0.76$. (c),(d) $\mathrm{\Delta }\sigma \equiv ⟨\sigma ⟩-{\sigma }_{\mathrm{Y}}$ as a function of shear rate with finite size scaling. The dashed lines show the HB law: $\mathrm{\Delta }\sigma \sim {\dot{\gamma }}^{1/{\beta }_{\mathrm{A}/\mathrm{B}}}$. Left: results for system A. Right: results for system B.

Figure 3

Finite size scaling of strain-based diffusion constant $\widehat{D}$ using exponent $\nu \approx 1.04$ associated with the avalanche correlation length $\xi$. Dashed lines represent the slope of $-1$ expected from the scaling argument. Results for (a) system A and (b) system B.

Figure 4

Schematic picture of (a) ST correlation length $\zeta$ and (b) avalanche correlation length $\xi$. Mobile particles (see SM for precise definition [23]) of all Im-INMs that correspond to active STs are highlighted in red. The results from a system with $N=2048$ under shear of the rate $\dot{\gamma }=2\times {10}^{-3}$ are shown. The copied images due to the periodic boundary conditions are also visualized around the original computational domain with lighter colors. Black arrows depict the eigenvectors.

Figure 5

Finite size scaling of the strain-based diffusion constant $\widehat{D}$ using the exponent $\tilde{\nu }=1/d$ associated with the ST correlation length $\zeta$. Dashed lines represent the slope of $-1$ expected from the scaling argument. (a) Results for system A. (b) Results for system B.