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

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.