Abstract. We study a simple model of spin network evolution motivated by the hypothesis that the emergence of classical spacetime from a discrete microscopic dynamics may be a self-organized critical process. Self-organized critical systems are statistical systems that naturally evolve without fine tuning to critical states in which correlation functions are scale invariant. We study several rules for evolution of frozen spin networks in which the spins labeling the edges evolve on a fixed graph. We find evidence for a set of rules which behaves analogously to sand pile models in which a critical state emerges without fine tuning, in which some correlation functions become scale invariant.

PACS numbers: 04.60.Pp, 04.60.−m, 05.65.+b, 89.75.Da

Print publication: Issue 9 (7 May 2008)
Received 14 November 2007, in final form 21 February 2008
Published 22 April 2008