Two-dimensional random surfaces are constructed by the mapping in d-dimensional space of a triangular network (of linear size L) with hierarchical bond structure. A relation between static properties of such surfaces and the resistance exponent, ζ, of two-dimensional inhomogeneous structures allows us to show that free surfaces have an average radius of gyration ξ∼Lζ/2 for L→∞. When a self-avoidance constraint is imposed, a Flory argument gives ξ∼L2/D with D=(2+d)/(2+(1/2ζ), and an upper critical dimension dc=8/ζ. Specific examples are discussed where exact, nontrivial values of ξ can be predicted by renormalization and scaling arguments. Universal, as well as nonuniversal, asymptotic regimes occur.
Hierarchical Random Surfaces
MARITAN, AMOS;STELLA, ATTILIO
1987
Abstract
Two-dimensional random surfaces are constructed by the mapping in d-dimensional space of a triangular network (of linear size L) with hierarchical bond structure. A relation between static properties of such surfaces and the resistance exponent, ζ, of two-dimensional inhomogeneous structures allows us to show that free surfaces have an average radius of gyration ξ∼Lζ/2 for L→∞. When a self-avoidance constraint is imposed, a Flory argument gives ξ∼L2/D with D=(2+d)/(2+(1/2ζ), and an upper critical dimension dc=8/ζ. Specific examples are discussed where exact, nontrivial values of ξ can be predicted by renormalization and scaling arguments. Universal, as well as nonuniversal, asymptotic regimes occur.Pubblicazioni consigliate
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