Selfavoiding and Planar Random Surfaces on the Lattice - INSPIRE

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Selfavoiding and Planar Random Surfaces on the Lattice

Apr, 1983

19 pages

Published in:

Nucl.Phys.B 225 (1983) 185-203

Published: 1983

DOI:

10.1016/0550-3213(83)90048-2

Report number:

NORDITA-83/15

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Abstract: (Elsevier)

We study models of self-avoiding (SARS) and of planar (PRS) random surfaces on a (hyper-) cubic lattice. If N γ ( A ) is the number of such surfaces with given boundary γ and area A , then N γ ( A ) = exp( β 0 A + o( A )), where β 0 is independent of γ. We prove that, for β > β 0 , 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.

LATTICE FIELD THEORY: RANDOM SURFACE
LATTICE FIELD THEORY: CRITICAL PHENOMENA
LATTICE FIELD THEORY: STRING TENSION
GAUGE FIELD THEORY
CORRELATION: LENGTH
ENTROPY
LATTICE FIELD THEORY: CONTINUUM LIMIT

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