Open AccessONE-DIMENSIONAL PERCOLATION PROBLEM WITH FURTHER NEIGHBOUR BONDS——REAL-SPACE RENORMALIZATION GROUP METHOD
Author(s) -
Tiecheng Li,
Zhao-Qing Zhang,
Pu Fu-Cho
Publication year - 1983
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.32.1273
Subject(s) - renormalization group , percolation (cognitive psychology) , scaling , physics , percolation critical exponents , percolation threshold , critical exponent , space (punctuation) , combinatorics , group (periodic table) , condensed matter physics , mathematical physics , mathematics , quantum mechanics , computer science , phase transition , geometry , electrical resistivity and conductivity , neuroscience , biology , operating system
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.