Self-organized critical behavior: the evolution of frozen spin networks model in quantum gravity

TL;DR

This paper investigates the evolution of frozen spin networks in quantum gravity, demonstrating self-organized criticality through a novel propagation rule where the changeable edge color exhibits power-law behavior, indicating potential cosmological inflation.

Contribution

Introduces a new propagation rule with variable edge color changes and verifies SOC behavior in frozen spin networks for the first time.

Findings

System exhibits power-law behavior indicating SOC

Variable edge color change influences network evolution

Potential link to cosmological inflation phenomena

Abstract

In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered evolution rule, the random edge model, is depending on choosing an edge randomly and changing the color of it by an even integer. Since the change of color generally violate the gauge invariance conditions imposed on the system, 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 integer is not a constant one as in previous works, but changeable with certain probability. In random edge model, we do find the evolution of the system under the propagation rule exhibits power-law behavior, which is suggestive of the self-organized criticality (SOC), and it is the first time to verify the SOC behavior in such evolution model for the frozen spin network. Furthermore, the increase of the average color of the spin network in time can show the nature of inflation for the universe.