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Universal scaling behavior in nature
The concept of self-organized critical (SOC) phenomena has been introduced some time ago to explain the frequent occurrences of scaling laws experienced in nature. The term SOC usually refers to a mechanism of slow energy accumulation and fast energy redistribution, driving a system toward a critical state. The prototype of SOC systems is the sand-pile model in which particles are randomly dropped onto a two dimensional lattice and the sand is redistributed by fast avalanches. Therefore in SOC models instead of tunig the parameters an inherent mechanism is responsible for driving it to criticality. SOC mechanism has been proposed to model earthquakes the evolution of biological systems, solar flare occurrence, fluctuations in confined plasma, snow avalanches and rain fall.
Diverging correlation length and scaling may also occur away from the phase transition point. For example in quantum matter near absolute zero temperature thermal equilibration can be obstructed in case of topological ordered ground states, where only the slow dynamical relaxation of defects pairs -- via annihilation-diffusion -- can occur (see example : C. Chamon, Phys. Rev. Lett. 94 040402 (2005)).