论文标题
接枝格子星星的熵指数
Entropic exponents of grafted lattices stars
论文作者
论文摘要
使用PERM算法，在数值上估计了在硬壁中的中央节点上接枝的半空间晶格星的表面熵指数。在正方形的半晶格中，验证了指数的确切值，包括理发师的缩放关系和$ 2 $标准的概括，分别具有一个和两个表面循环。这是关系\ [γ_{211} = 2 \，γ_{21}-γ_{20}，\]，其中$γ_{21} $和$γ_{211} $是与一个和两个表面上的$ 2 $ - star no coperts和$γ的表面熵指数，是$ 2 $ star and $γ_循环。该关系还在立方半晶格中进行了测试，估计表面熵指数高达$ 5 $标准，其中许多具有一个或多个表面环。 Barber's scaling relation and the relation \[ γ_{3111}=γ_{30}-3\,γ_{31}+3\,γ_{311} \] are also tested, where the exponents $\{γ_{31},γ_{311},γ_{3111}\}$ are of grafted $ 3 $ - 标准分别具有一个，两个或三个表面回路，$γ_{30} $是嫁接$ 3 $ - 标准的表面指数。
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 relation \[ γ_{211}=2\,γ_{21}-γ_{20},\] where $γ_{21}$ and $γ_{211}$ are the surface entropic exponents of a grafted $2$-star with one and two surface loops respectively, and $γ_{20}$ 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 \[ γ_{3111}=γ_{30}-3\,γ_{31}+3\,γ_{311} \] are also tested, where the exponents $\{γ_{31},γ_{311},γ_{3111}\}$ are of grafted $3$-stars with one, two or three surface loops respectively, and $γ_{30}$ is the surface exponent of grafted $3$-stars.
