Appearance of mother universe and singular vertices in random geometries

Białas, P.; Burda, Z.; Petersson, Bengt; J.Tabaczek,

doi:10.1016/s0550-3213(97)00226-5

Cited by 54 publications

(83 citation statements)

References 15 publications

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“…[8] that these phase transitions reflect the dynamics of the skeleton trees. Indeed, in BP theory the position of the minimum of F (φ) changes when one moves in the coupling space and a phase transition occurs when this minimum hits the boundary of the support of this function: the generic BP turn into crumpled structures i.e.…”

Section: Discussionmentioning

confidence: 82%

“…It is a subject of intrinsic interest and has already been studied by several authors [1]- [7]. A further motivation for developing these studies is provided by the recent suggestion [8] that important features of Euclidean quantum gravity can be inferred from those of the ensemble of branched polymers isomorphic to the ensemble of trees of baby universes connected by wormholes.…”

Section: Introductionmentioning

confidence: 99%

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Branched polymers with loops

Jurkiewicz¹,

Krzywicki²

1997

Physics Letters B

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We propose a classification of critical behaviours of branched polymers for arbitrary topology. We show that in an appropriately defined double scaling limit the singular part of the partition function is universal. We calculate this partition function exactly in the generic case and perturbatively otherwise. In the discussion section we comment on the relation between branched polymer theory and Euclidean quantum gravity.

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Section: Discussionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Branched polymers with loops

Jurkiewicz¹,

Krzywicki²

1997

Physics Letters B

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“…Many of the characteristics of the phase structure of simplicial gravity, described in the previous sections, are captured by a simple mean-field model -the balls-inboxes model [26]. This model consists of fixed number N of balls distributed into a variable number M of boxes, 1 ≤ M ≤ M max .…”

Section: "Balls In Boxes"mentioning

confidence: 99%

Lattice gravity and random surfaces

Þorleifsson

1999

Nuclear Physics B - Proceedings Supplements

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I review recent progress in simplicial quantum gravity in three and four dimensions, in particular new results on the phase structure of modified models of dynamical triangulations, the application of a strong-coupling expansion, and the benefits provided by including degenerate triangulations. In addition, I describe some recent numerical and analytical results on anisotropic crystalline membranes. Simplicial Quantum Gravity in D > 2The task of formulating a consistent theory of quantum gravity in four dimensions, hence unifying the two pillars of modern physics, general relativity and quantum mechanics, is a formidable one and still unresolved. Many different approaches have been tried (see e.g. Ref.[1]), some have led to a deeper understanding of the problem but, as of yet, none can claim much success. In this article I will review the status, and recent progress, of one such approach, namely the attempt to make sense of an Euclidean path-integral quantization of general relativity via a discretization known as dynamical triangulations.In Euclidean quantum gravity a path-integral is written as a formal sum over D-dimensional Euclidean geometries (metrics g µν )weighted by the Einstein-Hilbert actionG is the Newton's constant, Λ the cosmological constant and R the scalar curvature. However, this path-integral formulation faces some sever problems and unresolved questions:• the theory is non-renormalizable, • the action is unbounded from below, 1

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“…While they are originally associated with phase transitions of matter from the gas state to some liquid or solid state, they are also closely related to nucleation and coarsening phenomena. Examples of condensation appear in processes such as the formation of breath figures [1], Bose-Einstein condensation [2], polymer aggregation [3], but in a wider sense also in more generic systems like networks as the formation of clusters [4] through the accumulation of links on sites.…”

mentioning

confidence: 99%

“…Examples include refs. [2,4] mentioned above, but also processes such as wealth condensation [5] or traffic flow [6].…”

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confidence: 99%

Boundary-drive–induced formation of aggregate condensates in stochastic transport with short-range interactions

Nagel

Meyer‐Ortmanns

Janke

2015

EPL

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-We discuss the effects of particle exchange through open boundaries and the induced drive on the phase structure and condensation phenomena of a stochastic transport process with tunable short-range interactions featuring pair-factorized steady states (PFSS) in the closed system. In this model, the steady state of the particle hopping process can be tuned to yield properties from the zero-range process (ZRP) condensation model to those of models with spatially extended condensates. By varying the particle exchange rates as well as the presence of a global drift, we observe a phase transition from a free particle gas to a phase with condensates aggregated to the boundaries. While this transition is similar to previous results for the ZRP, we find that the mechanism is different as the presence of the boundary actually influences the interaction due to the non-zero interaction range.Condensation phenomena are observed in a broad range of physical processes. While they are originally associated with phase transitions of matter from the gas state to some liquid or solid state, they are also closely related to nucleation and coarsening phenomena. Examples of condensation appear in processes such as the formation of breath figures [1], Bose-Einstein condensation [2], polymer aggregation [3], but in a wider sense also in more generic systems like networks as the formation of clusters [4] through the accumulation of links on sites.For many such systems, the involved condensation process can be modeled as a stochastic transport process with a set of particles occupying a number of discrete sites. With particles representing microscopic to macroscopic objects and appropriate dynamics a wide spectrum of physical processes has been studied. Examples include refs. [2, 4] mentioned above, but also processes such as wealth condensation [5] or traffic flow [6].The zero-range process (ZRP) with condensation dynamics [7,8] is a well known paradigm of such transport processes. While it has a fully symmetric steady state, above some critical density ρ c the symmetry breaks spon-(a) E-mail: hannes.nagel@itp.uni-leipzig.de (b) E-mail: h.ortmanns@jacobs-university.de (c) E-mail: wolfhard.janke@itp.uni-leipzig.de taneously and a particle condensate emerges at a single site such that the density at the remaining sites stays critical. When short-range interactions are introduced, a similar condensation process can be observed with the main difference, that condensates can be spatially extended [9][10][11][12]. In this work, however, we shall consider condensation not as an effect in the steady state, but as a signature of a boundary induced phase transition. Such transitions can occur in driven systems, where the drive is implemented in terms of the interaction at the boundary of the system [13]. A well known transport process with such a transition is the totally asymmetric simple exclusion process (TASEP) [14,15], where a high-density, a lowdensity and a maximal-current phase exist [16]. For the ZRP, such effects of open boun...

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Appearance of mother universe and singular vertices in random geometries

Cited by 54 publications

References 15 publications

Branched polymers with loops

Branched polymers with loops

Lattice gravity and random surfaces

Boundary-drive–induced formation of aggregate condensates in stochastic transport with short-range interactions

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