二维Manhattan格点上端点附壁自避行走的计算机模拟

SELF-AVOIDING WALK ON TWO-DIMENSIONAL MANHATTAN LATTICE TERMINALLY ATTACHED TO A LINE: COMPUTER SIMULATION

采用精确计数法 ,计算了二维Manhattan格点上端点附壁自避行走的构象数CN,均方末端距R2 N,和均方回转半径Rg2 N,最长链长分别达到 5 0 ,5 0和 35步 .通过比率法和Pad啨近似法 ,处理精确计数数据得到有效配位数 μ =1.73377,标度指数γ =0 .934,ν =0 .7334.发现二维Manhattan格点上端点附壁自避行走的γ值和普通方格子上的相应值相同 ,且 μ值与二维Manhattan格点上的自由SAW的相应值一致 .由尺寸参数R2 N,R2 ∥ ,R2 ⊥,Rg2 N,Rg2 ∥ 和Rg2 ⊥ 随链长N的变化发现 ,壁对几何尺寸的影响十分明显 .

The total number of self avoiding walks terminally attached to a line on the two dimensional Manhattan lattice, C N, their mean square end to end distance R 2 N, and their mean square radius of gyration Rg 2 N , were exactly enumerated up to 50,50 and 35steps, respectively. The analysis of exact enumeration data using the ratio method and Dlog Pade approximant gave the connective constant μ =1.73377, the critical exponents γ =0.934 and ν =0.7334. It was found that the value of γ was in agreement with the corresponding value on the square lattice, and the value of μ was in agreement with the corresponding value for self avoiding walks on two dimensional Manhattan lattice. According to the change of the size parameters R 2 N, R 2 ∥,R 2 ⊥, Rg 2 N, Rg 2 ∥ and Rg 2 ⊥ with the step number N, it was concluded that the confined line affects the sizes apparently.