Non-perturbative renormalization group flows in two-dimensional quantum gravity

Renken, R.L.; Catterall, Simon; Kogut, John B.

doi:10.1016/0370-2693(94)01602-9

Cited by 11 publications

(12 citation statements)

References 8 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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“…One such operator is O = i log q i which corresponds to a set of higher derivative curvature interactions. The non-perturbative flows of this operator have been examined previously in the context of the LGB method [10].…”

Section: Higher Derivative Curvature Termmentioning

confidence: 99%

A real-space renormalization group for random surfaces

Þorleifsson

Catterall

1996

Nuclear Physics B

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We propose a new real-space renormalization group transformation for dynamical triangulations. It is shown to preserve geometrical exponents such as the string susceptibility and Hausdorff dimension. We furthermore show evidence for a fixed point structure both in pure gravity and gravity coupled to a critical Ising system. In the latter case we are able to extract estimates for the gravitationally dressed exponents which agree to within 2 − 3% of the KPZ formula.

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“…Presumably this should be true for block triangulations as well and, in two dimensions, the condition can be imposed easily to define a block spin renormalization group transformation [13,14]. This is accomplished as follows.…”

Section: Introductionmentioning

confidence: 99%