A real-space renormalization group for random surfaces

Þorleifsson, Guðmar; Catterall, Simon

doi:10.1016/0550-3213(95)00664-8

Cited by 21 publications

(24 citation statements)

References 27 publications

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“…In fact there is another equally valid reason to take them into account. In the dynamical lattice approach of 2-D gravity, there has been several (mostly numerical) attempts to perform real space renormalization [14,24,25,[46][47][48][49][50]. This amounts to replace a block of neighboring cells of the random lattice by a single, larger cell.…”

Section: Discussionmentioning

confidence: 99%

A scenario for the c > 1 barrier in non-critical bosonic strings

David

1997

Nuclear Physics B

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The c ≤ 1 and c > 1 matrix models are analyzed within large N renormalization group, taking into account touching (or branching) interactions.The c < 1 modified matrix model with string exponentγ > 0 is naturally associated with an unstable fixed point, separating the Liouville phase (γ < 0) from the branched polymer phase (γ = 1/2). It is argued that at c = 1 this multicritical fixed point and the Liouville fixed point coalesce, and that both fixed points disappear for c > 1. In this picture, the critical behavior of c > 1 matrix models is generically that of branched polymers, but only within a scaling region which is exponentially small when c → 1. Large crossover effects occur for c − 1 small enough, with a c ∼ 1 pseudo scaling which explains numerical results. * CNRS 1

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Section: Discussionmentioning

confidence: 99%

A scenario for the c > 1 barrier in non-critical bosonic strings

David

1997

Nuclear Physics B

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“…My motivation is two-fold. First, the coarse graining procedures developed by Johnston, Kownacki, and Krzywicki [30] and by Catterall, Renken, and Thorleifsson [35,36,39] for Euclidean dynamical triangulations and even the coarse graining procedure developed by Henson [27] for causal dynamical triangulations are in fact not well-suited to causal dynamical triangulations: the triangulation obtained after just a single iteration of the procedure is no longer necessarily a causal triangulation. (Indeed, the output of Henson's coarse graining procedure might not even be a simplicial manifold.)…”

Section: Construction Of the Renormalization Group Flowsmentioning

confidence: 99%

On a renormalization group scheme for causal dynamical triangulations

Cooperman

2016

Gen Relativ Gravit

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The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group schemein concert with finite size scaling analysis-is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in the first paper of this two-part series. As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.

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“…Additional evidence for this claim is obtained by applying a recently proposed Monte Carlo renormalization group method for blocking dynamical triangulations (node decimation [8]) to the model. Each triangulation is blocked by removing vertices at random and in the process the restrictions on the curvature are dropped so that the model flows into the wider class of combinatorial triangulations.…”

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confidence: 97%

Minimal dynamical triangulations of random surfaces

1997

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We introduce and investigate numerically a minimal class of dynamical triangulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the local coordination number, or equivalently intrinsic scalar curvature, leaves intact the fractal structure characteristic of generic dynamically triangulated random surfaces. Furthermore the Ising model coupled to minimal twodimensional gravity still possesses a continuous phase transition. The critical exponents of this transition correspond to the usual KPZ exponents associated with coupling a central charge c = 1 2 model to two-dimensional gravity.That two-dimensional (2D) quantum gravity can be regularized and studied using dynamical triangulations (DT) is well known [1] and has lead to extensive study of the properties of dynamically triangulated random surfaces (DTRS). Indeed, many of the properties of critical spin systems on such lattices have been shown to follow from continuum treatments of central charge c < 1 theories coupled to 2D-quantum gravity. Furthermore, this formulation has the advantage that it renders tractable the calculation of many features of these theories which are inaccessible to continuum methods. Foremost amongst these are questions related to the quantum geometry and fractal structure of the typical 2D manifolds appearing in the partition function [2].It has often been speculated that some of these models should also find a realization in condensed matter physics as models of membranes and/or interfaces with fluid in-plane degrees of freedom. The problem in trying to map such problems onto dynamically triangulated models, however, has always been the occurrence of large vertex coordination numbers in an arbitrary random graph -real condensed matter systems typically place a cut-off on the number of interactions allowed by the microscopic degrees of freedom. It is possible that such cut-offs are unimportant in the 1

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A real-space renormalization group for random surfaces

Cited by 21 publications

References 27 publications

A scenario for the c > 1 barrier in non-critical bosonic strings

A scenario for the c > 1 barrier in non-critical bosonic strings

On a renormalization group scheme for causal dynamical triangulations

Minimal dynamical triangulations of random surfaces

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