Evidence for a Disordered Critical Point in a Glass-Forming Liquid

Using computer simulations of an atomistic glass-forming liquid, we investigate the fluctuations of the overlap between a fluid configuration and a quenched reference system. We find that large fluctuations of the overlap develop as temperature decreases, consistent with the existence of the random critical point that is predicted by effective field theories. We discuss the scaling of fluctuations near the presumed critical point, comparing the observed behavior with that of the random-field Ising model. We argue that this critical point directly reveals the existence of an interfacial tension between amorphous metastable states, a quantity relevant both for equilibrium relaxation and for nonequilibrium melting of stable glass configurations.

Figure 1

(a) Dependence of the average overlap $⟨Q⟩$ on the field $\epsilon$ along various isotherms for $N=256$ (solid lines) and $N=150$ (dashed lines). The behavior is reminiscent of isotherms in a liquid-vapor system. (b) Total susceptibility $\chi (\epsilon ,T)$ for the same parameters, showing increasing fluctuations as temperature is reduced and system size is increased. (c) Temperature dependence of the field ${\epsilon }^{*}$ that maximizes $\chi$, indicating the boundary between low-$Q$ and high-$Q$ regimes. (d) Free energy $V(Q)$ for the same temperatures as in (a),(b) for $N=256$, with a dashed line indicating linear behavior.

Figure 2

(a) Overlap distributions $P(Q)$ measured along the ${\epsilon }^{*}(T)$ line for $N=256$ (solid lines); dotted lines are for $N=150$ and $T=0.6$ and 0.55. For the lowest temperature, a bimodal structure appears. (b) Behavior of $P(Q)$ for various $\epsilon$, increasing from low $\epsilon$ (blue) to $\epsilon ={\epsilon }^{*}$ (black) and large $\epsilon$ (purple) for $N=256$ and $T=0.55$.

Figure 3

(a) Sample-to-sample fluctuations of the distributions $P(Q)$ for $T=0.55$, $N=256$ evaluated at the average ${\epsilon }^{*}$. Colors indicate whether the samples are predominately in high-, intermediate, or low-$Q$ states. As expected for RFIM behavior, most distributions are unimodal, averaging to a total bimodal distribution (black). (b) Temperature dependence of the susceptibilities ${\chi }_{\text{dis}}$ and ${\chi }_T$ measured at ${\epsilon }^{*}$. The solid line is the RFIM prediction, Eq. (1).

Figure 4

(a) Comparison of distributions $P(Q)$ and $T=0.55$, for $T^{\prime }=T$ and $T^{\prime }=0.45$, at their corresponding fields ${\epsilon }^{*}$. (b) Comparison at $T=0.6$ between equilibrated ${\mathcal{C}}_0$ at $T^{\prime }=0.6$ and (biased) inactive ${\mathcal{C}}_0$. In both cases, the more stable states are associated with strongly bimodal $P(Q)$, indicating that coexistence between these low-energy states and the equilibrium fluid incurs a significant interfacial free-energy cost.