臺灣博碩士論文加值系統

在平面晶格上的不相交步行和不相交多邊形問題中，臨界指數和一些臨界
振幅的組合被認為是普適常數。而此研究的主要意圖，是藉由計算可果美
晶格上的臨界指數、臨界振幅的組合，而來驗證這些普適常數的正確性。
到目前為止，這些普適常數並沒有嚴格的數學證明，實驗上也不能測量。
但是從物理觀點上它們的值被精確地預測。我們的最後結果有些和預測值
非常接近，有些並不是非常接近預測值。

Critical exponents and some amplitude combinations of self-
avoiding walks and polygons are believed to be universal. The
main intension of this research is to check whether those
constants on planar lattice are universal by studing the kagome
lattice. We write a Fortran program to enumerate the self-
avoiding polygon, the mean square radius of gyration of self-
avoiding polygon and the moments of the area of self-avoiding
polygon simultaneously. We apply some methods of series
analysis on those series to get the values of the estimation.
The universal constants as metioned above have not been
rigorously proved but their values have been predicted. Some
estimation values are very close to the predicted values but
some not.