TY - JOUR

T1 - The Hausdorff dimension of surfaces in two-dimensional quantum gravity coupled to Ising minimal matter

AU - Bowick, Mark J.

AU - John, Varghese

AU - Thorleifsson, Gudmar

N1 - Funding Information:
We would like to thank Jan Ambjorn, Kostas Anagnostopoulos and Nobuyuki Ishibashi for detailed discussions of non-critical string field theory and issues related to the fractal dimensionality of two-dimensional gravity. We have benefited as well from useful conversations with Simon Catterall, Marco Falcioni and Fransois David. This researchw as supported by the Department of Energy, USA, under contractN o.DE-FG02-8540237 and by researchf unds from Syracuse University.

PY - 1997/6/26

Y1 - 1997/6/26

N2 - Within the framework of string field theory the intrinsic Hausdorff dimension dH of the ensemble of surfaces in two-dimensional quantum gravity has recently been claimed to be 2m for the class of unitary minimal models (p = m+1, q = m). This contradicts recent results from numerical simulations, which consistently find dH ≈ 4 in the cases m = 2, 3, 5 and ∞. The string field calculations rely on identifying the scaling behavior of geodesic distance and area with respect to a common length scale l. This length scale is introduced by formulating the models on a disk with fixed boundary length l. In this paper we study the relationship between the mean area and the boundary length for pure gravity and the Ising model coupled to gravity. We discuss how this relationship is modified by relevant perturbations in the Ising model. We discuss how this leads to a modified value for the Hausdorff dimension.

AB - Within the framework of string field theory the intrinsic Hausdorff dimension dH of the ensemble of surfaces in two-dimensional quantum gravity has recently been claimed to be 2m for the class of unitary minimal models (p = m+1, q = m). This contradicts recent results from numerical simulations, which consistently find dH ≈ 4 in the cases m = 2, 3, 5 and ∞. The string field calculations rely on identifying the scaling behavior of geodesic distance and area with respect to a common length scale l. This length scale is introduced by formulating the models on a disk with fixed boundary length l. In this paper we study the relationship between the mean area and the boundary length for pure gravity and the Ising model coupled to gravity. We discuss how this relationship is modified by relevant perturbations in the Ising model. We discuss how this leads to a modified value for the Hausdorff dimension.

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U2 - 10.1016/S0370-2693(97)00531-5

DO - 10.1016/S0370-2693(97)00531-5

M3 - Article

AN - SCOPUS:0039375910

SN - 0370-2693

VL - 403

SP - 197

EP - 202

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 3-4

ER -