Entropic exponents of grafted lattices stars

Abstract

The surface entropic exponents of half-space lattice stars grafted at their central nodes in a hard wall are estimated numerically using the PERM algorithm. In the square half-lattice the exact values of the exponents are verified, including Barber's scaling relation and a generalisation for 2-stars with one and two surface loops respectively. This is the relationwhere γ21 and γ211 are the surface entropic exponents of a grafted 2-star with one and two surface loops respectively, and γ20 is the surface entropic exponent with no surface loops. This relation is also tested in the cubic half-lattice where surface entropic exponents are estimated up to 5-stars, including many with one or more surface loops. Barber's scaling relation and the relation γ3111 = γ30 − 3 γ31 + 3 γ311 are also tested, where the exponents {γ31, γ311, γ3111} are of grafted 3-stars with one, two or three surface loops respectively, and γ30 is the surface exponent of grafted 3-stars.