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In quantum gravity, we study the evolution of a two-dimensional planar openfrozen spin network, in which the color (i.e. the twice spin of an edge)labeling edge changes but the underlying graph remains fixed. The mainlyconsidered evolution rule, the random edge model, is depending on choosing anedge randomly and changing the color of it by an even integer. Since the changeof color generally violate the gauge invariance conditions imposed on thesystem, detailed propagation rule is needed and it can be defined in many ways.Here, we provided one new propagation rule, in which the involved even integeris not a constant one as in previous works, but changeable with certainprobability. In random edge model, we do find the evolution of the system underthe propagation rule exhibits power-law behavior, which is suggestive of theself-organized criticality (SOC), and it is the first time to verify the SOCbehavior in such evolution model for the frozen spin network. Furthermore, theincrease of the average color of the spin network in time can show the natureof inflation for the universe.Comment: 5 pages, 5 figure

SELF-ORGANIZED CRITICAL BEHAVIOR: THE EVOLUTION OF FROZEN SPIN NETWORKS MODEL IN QUANTUM GRAVITY