Appearence of Mother Universe and Singular Vertices in Random Geometries

Details Appearence of Mother Universe and Singular Vertices in Random Geometries Appearence of Mother Universe and Singular Vertices in Random Geometries

1996-08-07

arxiv.org/abs/hep-lat/9608030v1

Nucl.Phys. B495 (1997) 463-476

Physics

High Energy Physics

High Energy Physics - Lattice

13 latex pages + 6 ps fig. + elsart.cls, uufiles-encoded

Scientific paper

10.1016/S0550-3213(97)00226-5

We discuss a general mechanism that drives the phase transition in the canonical ensemble in models of random geometries. As an example we consider a solvable model of branched polymers where the transition leading from tree- to bush-like polymers relies on the occurrence of vertices with a large number of branches. The source of this transition is a combination of the constraint on the total number of branches in the canonical ensemble and a nonlinear one-vertex action. We argue that exactly the same mechanism, which we call constrained mean-field, plays the crucial role in the phase transition in 4d simplicial gravity and, when applied to the effective one-vertex action, explains the occurrence of both the mother universe and singular vertices at the transition point when the system enters the crumpled phase.

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