Singular vertices in the strong coupling phase of four-dimensional simplicial gravity

Hotta, T.; Izubuchi, Taku; Nishimura, Jun

doi:10.1016/0920-5632(96)00132-6

Cited by 16 publications

(12 citation statements)

References 14 publications

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“…Comparison of figures 1,2,3 with figure 4 and those in [6] clearly shows a great similarity between simplicial 4d gravity, minbu trees, and branched polymers, not only in the elongated phase, but also beyond the transition into the crum- pled phase. It seems apparent that in all these cases the constrained mean-field mechanism plays the crucial role in the transition.…”

Section: Simplicial Gravitymentioning

confidence: 66%

“…For κ 2 below the critical value [5], simplicial gravity enters the crumpled phase. So-called singular vertices occur on the typical geometry, vertices of a large order that grows linearly with the volume of the ensemble [6,7]. Because of this, almost the whole universe is in the neighbourhood of these singular vertices, which means that the average geodesic distances between simplices depends weakly if at all on the universe's volume.…”

Section: Introductionmentioning

confidence: 99%

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Appearance of mother universe and singular vertices in random geometries

et al. 1997

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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. ITFA

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Section: Simplicial Gravitymentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Appearance of mother universe and singular vertices in random geometries

et al. 1997

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“…In the elongated phase it is effectively described by the Branched Polymer model [4]. In the crumpled phase is characterized by the appearance of a singular vertices which gather around them an extensive part of the volume [5,6]. The transition between those two phases is of first order [7,8].…”

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confidence: 99%

Collapse of 4D random geometries

Białas¹,

Burda

1998

Physics Letters B

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We extend the analysis of the Backgammon model to an ensemble with a fixed number of balls and a fluctuating number of boxes. In this ensemble the model exhibits a first order phase transition analogous to the one in higher dimensional simplicial gravity. The transition relies on a kinematic condensation and reflects a crisis of the integration measure which is probably a part of the more general problem with the measure for functional integration over higher (d > 2) dimensional Riemannian structures.Recently we have proposed a scenario for the phase transition in higher dimensional simplicial quantum gravity based on the balls-in-boxes model [1, 2] also called Backgammon model in a different context [3]. It has been established that simplicial gravity has two phases: crumpled and elongated. In the elongated phase it is effectively described by the Branched Polymer model [4]. In the crumpled phase is characterized by the appearance of a singular vertices which gather around them an extensive part of the volume [5,6]. The transition between those two phases is of first order [7,8]. The constrained-mean-field interpretation based on Backgammon model captures all those features except the order of the transition.In this letter we show that the modified balls-in-boxes model undergoes a first order phase transition of the same type as in simplicial gravity.We start with a brief review of the properties the Backgammon model. The model describes N balls distributed in M boxes. The partition function reads [2,3]:

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“…The model has been introduced as a mean field approximation to lattice gravity [1,2]. Despite its simplicity, the model captures the main features of the phase transition observed in lattice Euclidean quantum gravity models (ie dynamical triangulations) such as the discontinuity of the transition [3,4] and the appearance of singular structures [5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%