二维Manhattan格点上端点附壁自避行走的计算机模拟

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R^2N，和均方回转半径Rg^2N，最长链长分别达到50，50和35步。通过比率法和Pade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，v＝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R^2N,R^2//,R^2┻，Rg^2N,Rg^2//和Rg^2┻随链长N的变化发现，壁对几何尺寸的影响十分明显。

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

The total number of self-avoiding walks terminally attached to a line on the two-dimensional Manhattan lattice, CN, their mean square end-to-end distance R2N, and their mean square radius of gyration Rg2N, 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 v = 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 R2N, R2∥, R2⊥, Rg2N, Rg2∥ and Rg2⊥ with the step number N, it was concluded that the confined line affects the sizes apparently.