1996/08/07 by P. Białas, P. Bialas, Z. Burda +2 · 4 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Microtubule and mitosis dynamics #hep-lat
paper · pdf · doi:10.1016/s0550-3213(97)00226-5
published as Nucl.Phys. B495 (1997) 463-476 · 13 latex pages + 6 ps fig. + elsart.cls, uufiles-encoded
arxiv created 1996/08/07 · openalex publication_date 1997/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.