Self-avoiding and planar random surfaces on the lattice |
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Authors: | B Durhuus J Fröhlich T Jonsson |
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Institution: | The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark;Theoretical Physics, ETH-Hönggerverg, CH-8093 Zürich, Switzerland;Nordita, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark |
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Abstract: | We study models of self-avoiding (SARS) and of planar (PRS) random surfaces on a (hyper-) cubic lattice. If Nγ(A) is the number of such surfaces with given boundary γ and area A, then Nγ(A) = exp(β0A + o(A)), where β0 is independent of γ. We prove that, for β > β0, the string tension is finite for the SARS model and strictly positive for the PRS model and that in both models the correlation length (inverse mass) is positive and finite. We discuss the possibility of the existence of a critical point and of a roughening transition. Estimates on intersection probabilities for random surfaces and connections with lattice gauge theories are sketched. |
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