Affiliation:
1. Newman Laboratory for Nuclear Studies, Cornell University, Ithaca, N.Y. 14853–5001, USA
Abstract
In this paper we compute exactly, using the scaling properties of the Liouville theory, the Hausdorff dimension of the continuous random surfaces of Polyakov for D≤1. We find that for D<1, the mean square size of the surface grows as a logarithm of the area of the surface as well as the area of the surface raised to a power, the power being minus the string susceptibility. For D=1 the behavior changes, as expected, because the model undergoes a phase transition. In that case we find that the mean square size of the surface behaves as a combination of terms that grow as a logarithm of the area as well as its square, in qualitative agreement with the results of numerical experiments in discrete models.
Publisher
World Scientific Pub Co Pte Lt
Subject
Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics
Cited by
40 articles.
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