二维晶格上Kadanoff分块及重整化群方法

Kadanoff Blocks and Renormalization Group Approach to Two-Dimensional Lattice

对二维晶格上的Kadanoff分块进行了全面分析 ,给出了划分的一般规律 得出元块选择的非任意性和含相同元块选择不惟一等结论 ,并给出正三角形格子和正方形格子下元块中格点数目的允许值 同时 ,利用重整化群方法对 9点、13点元块进行了计算 ,得到了相应的不动点和各种临界指数 ,并与其它计算结果进行了比较 结果表明 。

The renormalization group transformation and Kadanoff construction are applied to two\|dimensional lattices. The general rule for Kadanoff construction and permitted site’s number are given. The fixed points and critical exponents are then calculated for the blocks with 9 and 13 sites. The comparison is made between the results and those obtained by the exact solution. The result shows that the calculation precision tends to be raised with increasing of the site’s number in the construction.