Intrinsic and extrinsic geometry of random surfaces

Details Intrinsic and extrinsic geometry of random surfaces Intrinsic and extrinsic geometry of random surfaces

1991-11-05

arxiv.org/abs/hep-th/9111011v1

Phys.Lett. B278 (1992) 89-93

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

10.1016/0370-2693(92)90716-H

We prove that the extrinsic Hausdorff dimension is always greater than or equal to the intrinsic Hausdorff dimension in models of triangulated random surfaces with action which is quadratic in the separation of vertices. We furthermore derive a few naive scaling relations which relate the intrinsic Hausdorff dimension to other critical exponents. These relations suggest that the intrinsic Hausdorff dimension is infinite if the susceptibility does not diverge at the critical point.

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