A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS

数学物理学报(英文版) ›› 1986, Vol. 6 ›› Issue (3): 305-319.

A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS

张昭庆, 蒲富恪, 李伯臧

Institute of Physics, Chinese Academy of Sciences, Beijing

收稿日期:1984-04-09 出版日期:1986-09-25 发布日期:1986-09-25

A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS

Zhang Zhaoqing, Pu Fucho, Li Bozang

Institute of Physics, Chinese Academy of Sciences, Beijing

Received:1984-04-09 Online:1986-09-25 Published:1986-09-25

摘要/Abstract

摘要： The rigorous proof of the relation det A^(L)=-[Π_i=1^L q_iⁱ](1+q₁f_L(q₁,q₂,…,q_L))is given. This relation has been used to obtain the exact critical surface and the correlation length exponents of the one-dimensional directed bond percolation problem with bonds connecting 1~Lth nearest neighbours. A^(L) is related to the transfer-matrix by (7). q_i is related to the occupation probability of the i-th nearest neighbour bond p_i by q_i=1-p_i (i=1, 2, …, L). f_L is a multi-varlable polynomial in q_i's.

张昭庆, 蒲富恪, 李伯臧. A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS[J]. 数学物理学报(英文版), 1986, 6(3): 305-319.

Zhang Zhaoqing, Pu Fucho, Li Bozang. A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS[J]. Acta mathematica scientia,Series B, 1986, 6(3): 305-319.

A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS

A DETERMINANT FOR THE TRANSFER MATRIX OF THE ONE-DIMENSIONAL DIRECTED BOND PERCOLATION WITH FURTHER NEIGHBOUR BONDS

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