Self-organized criticality

Albert Diaz-Guilera

The phenomenon known as self-organized criticality is related to systems which spontaneously (self organized) evolve towards a stationary state without time and length characteristic scales; it is named critical because their analogies with critical phenomena, widely studied in equilibrium. The main differences are that now one deals with non-equilibrium systems, and hence equilibrium statistical mechanics can not be used, and that criticality appears without the necessity of tuning any external parameter. Follow this link to view some simple models.

Within this subject our contributions can be split in two distinct parts:

1. Analysis of critical exponents: On one hand, we have performed extensive numerical simulations in order to measure the critical exponents. These exponents give the basic behavior of the different magnitudes describing the system. On the other, we have done theoretical calculations by means of the dynamic renormalization group, arriving to analytical expressions for these exponents.  

2. Relation between self-organized criticality and synchronization: Two phenomena, that in principle have nothing to do with each other, like self-organized criticality and synchronization (see next paragraphs) can be present simultaneously in the same