Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Abstract

By finding local minima of an enthalpy-like energy, we can generate jammed packings of frictionless spheres under constant shear stress $\sigma$ and obtain the yield stress $\sigma_y$ by sampling the potential energy landscape. For three-dimensional systems with harmonic repulsion, $\sigma_y$ satisfies the finite size scaling with the limiting scaling relation $\sigma_y\sim\phi - \phi_{_{c,\infty}}$, where $\phi_{_{c,\infty}}$ is the critical volume fraction of the jamming transition at $\sigma=0$ in the thermodynamic limit. The width or uncertainty of the yield stress decreases with decreasing $\phi$ and decays to zero in the thermodynamic limit. The finite size scaling implies a length $\xi\sim (\phi-\phi_{_{c,\infty}})^{-\nu}$ with $\nu=0.81\pm 0.05$, which turns out to be a robust and universal length scale exhibited as well in the finite size scaling of multiple quantities measured without shear and independent of particle interaction. Moreover, comparison between our new approach and quasi-static shear reveals that quasi-static shear tends to explore low-energy states.