Branched polymers with loops

Jurkiewicz, J.; Krzywicki, A.

doi:10.1016/s0370-2693(96)01559-6

Cited by 28 publications

(49 citation statements)

References 16 publications

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“…(6.1) to the value of branched polymer phase d F = 2, γ s = 1/2 [44,45,46]. It is interesting to measure the change of fractal dimension very accurately in this delicate region near c ≈ 1.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Kawamoto

Yotsuji

2002

Nuclear Physics B

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We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for −2 ≤ c ≤ 1. We reformulate Q-state Potts model into the model which can be identified as a weighted percolation cluster model and can make continuous change of Q, which relates c, on the dynamically triangulated lattice. The c-dependence of the critical coupling is measured from the percolation probability and susceptibility. The c-dependence of the string susceptibility of the quantum surface is evaluated and has very good agreement with the theoretical predictions. The c-dependence of the fractal dimension based on the finite size scaling hypothesis is measured and has excellent agreement with one of the theoretical predictions previously proposed except for the region near c ≈ 1.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Kawamoto

Yotsuji

2002

Nuclear Physics B

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“…We also list some open questions. In this paper, when necessary, we make use of some results, found in a different context, scattered in earlier publications we have coauthored [15][16][17][18]. We believe, that it is useful to adapt these results to the present context, putting them in a new perspective and making them accessible to a different community.…”

Section: Introductionmentioning

confidence: 99%

Statistical ensemble of scale-free random graphs

2001

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A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is characterized by two global parameters, the fractal and the spectral dimensions, which are explicitly calculated. It is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified. The stability of the scale-free regime is also considered: when it breaks down, either a scale is spontaneously generated or else, a "singular" node appears and the graphs become crumpled. A new computer algorithm to generate these random graphs is proposed. Possible generalizations are also discussed. In particular, more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary (degenerate) scale-free random graphs.

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“…Another idea consists in introducing matter fields [2]. Indeed, in the continuum formalism, one can argue that adding conformal matter fields in 4d has the effect similar to that obtained by reducing their number in 2d [9] and might therefore bring one from the branched polymer to a physical phase (analogous to the Liouville phase in 2d).…”

Section: Introductionmentioning

confidence: 99%

4d Simplicial quantum gravity: matter fields and the corresponding effective action

et al. 1998

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Four-dimensional simplicial quantum gravity is modified either by coupling it to U (1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although the two modifications of the standard pure-gravity model are apparently very distinct, they produce strikingly similar results, as far as the geometry of random manifolds is concerned. In particular, for an appropriate choice of couplings, the branched polymer phase is replaced by a crinkled phase, characterized by the susceptibility exponent γ < 0 and the fractal dimension d H > 2. The quasi-equivalence between the two models is exploited to get further insight into the extended phase diagram of the theory.

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Branched polymers with loops

Cited by 28 publications

References 16 publications

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Statistical ensemble of scale-free random graphs

4d Simplicial quantum gravity: matter fields and the corresponding effective action

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