-
应用实空间重正群方法于一维具L-近邻键的点-渗流及键-渗流模型,得到类-温度标度率与类-场标度率,再利用普适标度律得到全部临界指数的精确结果。对于点-渗流模型有αp=2-L,βp=0,γp=L,δp=∞,ηp=1及vp=L。这与生成函数方法结果一致;对于键-渗流模型有αp=2-(L(L+1))/2,βp=0,γp=(L(L+1))/2,δp=∞,ηp=1及vp=(L(L+1))/2,其中的“热”临界指数与转移矩阵方法结果一致,磁临界指数是新的结果。由点-渗流及键-渗流模型求出Suzuki的弱普适律的重正化临界指数为φ≡(2-α)/v=1,β≡β/v=0,γ≡γ/v=1,δ≡δ=∞及η≡η=1。即重正化的临界指数不仅与L无关,而且也不依赖于是点抑键的渗流模型,即普适律对Suzuki重正化临界指数仍得以保持。One-dimensional site and bond percolation problems with bonds connecting Lth nearest neighbors are studied by using real-space renormalization group method. Exact thermal-like and field-like scaling powers are found. Using the scaling relations we obtain all the critical exponents. For the site percolation, we have ap= 2-L, βp=0,γp= L, δp= ∞, ηp = 1 and vp = L which are consistent with the results obtained by using generating function method. For the bond percolation, we have ap = 2-(L(L+1))/2,βp= 0, γp= L, δp =∞, ηp= 1 and vp= L where the "thermal" exponents are consistent with the results obtained by using transfer matrix method. Magnetic exponents found here are new results. Suzuki's renormalized ex-ponents are φ≡(2-α)/v = 1, β≡β/v = 0, γ≡γ/v = 1, δ≡δ=∞ and η≡η=1 which are independent of both L and site or bond percolations.
计量
- 文章访问数: 5777
- PDF下载量: 442
- 被引次数: 0
下载:
