Thermal activation drives a finite-size crossover from scale-free to runaway avalanches in amorphous solids

Abstract

We investigate thermal avalanche dynamics in amorphous solids using elastoplastic models with local activation rules and no external driving. Dynamical heterogeneities, quantified through persistence measurements and the associated four-point susceptibility $χ_4$, reveal the emergence of correlated spatiotemporal rearrangements as temperature is varied. As temperature increases, avalanche statistics evolve from scale-free behavior with exponential cutoffs to regimes dominated by system-spanning runaway events. We identify a system-size-dependent critical temperature $T_c(L)$ that separates intermittent avalanche dynamics from thermally assisted flow, where self-sustained avalanches transiently fluidize the system. We show that $T_c(L)$ decreases algebraically with increasing system size, suggesting that in the thermodynamic limit arbitrarily small but finite temperatures may destabilize the intermittent regime. The relation between avalanche size and duration resembles that in sheared systems, whereas the statistics of minimal distances to yielding reveal a temperature-driven reorganization of marginal stability absent in strictly driven overdamped dynamics. Our results demonstrate that thermal activation alone can generate a finite-size-controlled instability scale in disordered elastic media.

Figures (10)

• Figure 1: Comparison of the cores of extremal and fully thermal dynamics. The schematic curves show the a priori probabilities of thermal activation of the elastoplastic blocks during the avalanche dynamics. (a) Extremal dynamics, (b) Fully thermal dynamics.
• Figure 2: Plastic activity map during a thermal avalanche. The map is constructed by using the number of plastic activations $S_{A}(i)$ of each site $i\equiv(x,y)$ during an individual avalanche. The color scale on the right indicates the number of activation per site. The parameters used for this example are $T = 0.0042$ and $L = 128$.
• Figure 3: Persistence, relaxation time and dynamical susceptibility. Panel (a) illustrates the mean persistence curve, $\langle p(t) \rangle$, for various finite temperatures at a fixed system size. Panel (b) shows the relaxation time $\tau_{\alpha}$ as a function of $1/T$. The blue dashed line corresponds to an Arrhenius fit of the form $\tau_{\alpha} \propto \exp\left[\frac{0.013}{T}\right]$. The gray dashed line indicates the crossover inverse temperature $1/T^*$, marking the onset of Arrhenius-like behavior in the curve. Panel (c) displays $\chi_4$, as defined by Eq. \ref{['eq:chi4']} for the different temperatures in this analysis $T \in [0.0004, 0.008]$ The inset shows $\chi_4^{\textbf{peak}}$ versus $T$. The blue dashed line corresponds to a power-law fit, $\chi_4^{\textbf{peak}} \sim T^{-0.8}$. System size is $L=128$.
• Figure 4: Extremal dynamics Avalanche size and duration distributions for a fixed system size ($L=256$) and $x_0=$[0.001, 0.003, 0.010, 0.020, 0.021, 0.022, 0.025, 0.030, 0.040, 0.050] in the extremal dynamics protocol. The critical value is $x_c\approx 0.022$. Curves in grayscale correspond to $x_0>x_c$, and the gray dashed line marks the maximum avalanche size, $S_{\text{max}}$. Panel (a) shows the distribution of avalanche sizes $P(S)$, (b) the distribution of the total number of activations $P(S_A)$, and (c) the distribution of avalanche durations $P(D)$.
• Figure 5: Partial contributions to the avalanche size distributions $P(S)$ and $P(S_A)$ in the extremal dynamics for $L=256$ and $x_0=0.04$. Red circles represent the distribution of avalanches with durations below a threshold $D^{*}\simeq900$, while blue circles denote the distribution of avalanches exceeding $D^{*}$. Gray squares illustrate the distribution encompassing all avalanches.