Kinetic glass behavior in a diffusive model

Three properties of the Edwards-Anderson model with mobile bonds are investigated which are characteristic of kinetic glasses. First is two-time relaxation in aged systems, where a significant difference is observed between spin and bond autocorrelation functions. The spin subsystem does not show two-time behavior, and the relaxation is stretched exponential. The bond subsystem shows two-time behavior, with the first relaxation nearly exponential and the second similar to the spin one. Second is the two-temperature behavior, which can be tuned by bond dilution through the full range reported in the literature. Third is the rigid-to-floppy transition, identified as a function of bond dilution. Simple Glauber Monte Carlo evolution without extraneous constraints reproduces the behavior of classical kinetic simulations, with the bond (spin) degree of freedom corresponding to configurational (orientational) disorder.

Figure 1

Spin and bond autocorrelation functions in an aged sample. In each pair of curves, the bond autocorrelation is the one with the plateau at intermediate times. The solid, dashed, dotted, and dot-dashed curves correspond to temperatures $T∕J=0.05$, 0.15, 0.30, and 0.50, respectively. Each Monte Carlo step (MCS) consists of a spin and a bond update per site.

Figure 2

Violations of the fluctuation-dissipation theorem for an (a) Gaussian and (b) bimodal distribution. (a) Bottom to top: $T∕J=0.05,0.01,0.015,0.2,0.25,0.3,0.4,0.5,0.6$, respectively. (b) Top to bottom: $p_0=100\%,90\%,80\%,70\%,60\%,40\%,30\%,20\%,10\%$, respectively, at $T∕J=0.2$.

Figure 3

Rigid-to-floppy transition. The fraction of indifferent spins is shown as a function of bond dilution. The minimum corresponds to the least-strained system. The inset shows the minimum as a function of temperature.