Structural signature of jamming transition in thermal amorphous systems

In thermal amorphous systems, the first peak of the pair correlation function $g(r)$ shows a maximum height $g_1^{\rm max}$ at a volume fraction $\phi=\phi_v$ that increases with the temperature. $g_1^{\rm max}$ diverges at the T=0 jamming transition at $\phi=\phi_c$. Molecular dynamics simulations show that some typical quantities, such as the pressure, bulk modulus, shear modulus, and boson peak frequency that behave power law scalings with $\phi-\phi_c$ in marginally jammed solids at T=0, all show scalings with $\phi-\phi_c$ when $\phi > \phi_v$, while the scalings break down when $\phi < \phi_v$. The presence of $g_1^{\rm max}$ is thus not only a thermal vestige of the T=0 jamming transition, but more importantly the structural signature of the jamming transition.