TY - JOUR
T1 - Self-avoiding and planar random surfaces on the lattice
AU - Durhuus, Bergfinnur
AU - Fröhlich, Jürg
AU - Jónsson, Þórður
N1 - Copyright © 1983 Published by Elsevier B.V.
PY - 1983/10/31
Y1 - 1983/10/31
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/0040616118
U2 - 10.1016/0550-3213(83)90048-2
DO - 10.1016/0550-3213(83)90048-2
M3 - Article
SN - 0550-3213
VL - 225
SP - 185
EP - 203
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
IS - 2
ER -