论文信息 - Phase boundary for planar site-bond percolation problems from a generalised star-triangle transformation

Phase boundary for planar site-bond percolation problems from a generalised star-triangle transformation

On the basis of a generalised star-triangle transformation and of existing conjectures concerning the critical point of some planar Potts models, the phase boundary is determined for the combined site-bond percolation problem on a number of lattices, including the triangular and the honeycomb lattice. As a special case, the critical probability for the honeycomb site problem is found to be pc-1/ square root 2.

I. Kondor

[1] F. Y. Wu,et al. On the triangular Potts model with two- and three-site interactions , 1980 .

[2] F. Y. Wu. Critical point of planar Potts models , 1979 .

[3] M. Schick,et al. First and Second Order Phase Transitions in Potts Models: Renormalization - Group Solution , 1979 .

[4] J. Essam. Potts models, percolation, and duality , 1979 .

[5] W. Strieder,et al. Effective-medium theory of the conductivity for a random-site honeycomb lattice , 1979 .

[6] H. Stanley,et al. Site-Bond Correlated-Percolation Problem: A Statistical Mechanical Model of Polymer Gelation , 1979 .

[7] R. Baxter,et al. Triangular Potts model at its transition temperature, and related models , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8] R. Joseph,et al. Exact transition temperature of the Potts model with q states per site for the triangular and honeycomb lattices , 1974 .

[9] J. W. Essam,et al. Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions , 1964 .