Critical slowing down in thermal soft-sphere glasses via energy minimization

Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we show that the terminal relaxation times τ for FIRE energy minimization of soft-sphere glasses exhibit thermal onset as samples become increasingly well-equilibrated. Although τ(ϕ) can decrease by orders of magnitude as equilibration proceeds and the jamming density ϕ_ J increases via thermal onset, it always scales as τ(ϕ) ∼ (ϕ_ J - ϕ)^-2∼ [Z_ iso - Z_ ms(τ)]^-2, where ϕ_ J is the jamming density and Z_ ms(τ) is the average coordination number of particles satisfying a minimal local mechanical stability criterion (Z ≥ d+1) at the top of the final potential-energy-landscape (PEL) sub-basin the system encounters. This scaling allows us to collapse τ datasets that look very different when plotted as a function of ϕ, and to address a closely related question: how does the character of the PEL basins that dense thermal glasses most typically occupy evolve as the glasses age at constant ϕ and T?