Aging in a Model of Self-Organized Criticality

摘要: Temporal autocorrelation functions for avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical simulations show that they decay as power laws with two distinct regimes separated by a time scale which is waiting time, or age, of avalanche. Thus, timetranslational invariance dynamically broken. The critical exponent initial familiar stationary dynamics while new late-time appears. This characterizes nonstationary regime has not been previously considered context self-organized criticality. [S0031-9007(97)03663-6] PACS numbers: 64.60.Lx, 05.40. + j, 05.70.Ln, 87.10. e Self-organized criticality (SOC) [1] describes general property slowly driven dissipative systems many degrees freedom reach state where evolve intermittently terms bursts spanning all scales up system size. Many natural avalanchelike phenomena have represented using this idea, including earthquakes, extinction events biological evolution, and landscape formation [2]. Recently, SOC observed controlled laboratory experiments on rice piles [3]. Theoretical models [4] are related variety different physical universality [5]. emergence long-term memory demonstrated analytically multitrait evolution [6], variant [7]. Here we exhibits reminiscent [8]. We numerically measure two-time observe power-law regimes. early dynamics. characterizing history-dependent relaxation model. separating age Rescaling autocorrelations measured units respective collapses data onto scaling function single variable. signals breaking time-translational arising from system’s ability store information past over arbitrarily long times. “Aging” an important phenomenon experimentally materials depends previous history [9]. For instance, consider spin glass quenched below transition at t › 0 presence small magnetic field. Throughout sample, domains various pure states develop grow characteristic size Rstd. At tw, field turned off response form its remanent magnetization measured. Initially, only sensitive pure, quasiequilibrium their domains. But after additional spans entire slows down when it experiences nonequilibrium sample possesses whole. A simple holds some [10]. given