Triangular and Honeycomb Lattices Bond-Diluted Ising Ferromagnet: Critical Frontier

摘要

Within a real space renormalization group framework (12 different procedures, all of them using star-triangle and duality-type transformations) accurate approximations for the critical frontiers associated with the quenched bond-diluted first-neighbour spin- exp 1 / sub 2 Ising ferromagnet on triangular and honeycomb lattices are calculated. All of them provide, in both pure bond percolation and pure Ising limits, the exact critical points and exact or almost exact derivatives in the p-t space (p is the bond independent occupancy probability and t tanh J/k(sub B)T). The best numerical proposals lead to the exact derivative in the pure percolation limit (p = p(sub c)) and, in what concerns the pure Ising limit (p = 1) derivative, to a 0.15% error for the triangular lattice and to a 0.96% error for the honeycomb one; in the intermediate region (p(sub c) < p < 1), where the exact critical frontiers are still unknown, the worst error in the t-variable (for fixed p) is estimated to be less than 0.27% for the triangular lattice and to a 0.14% for the honeycomb one. Further more it is exhibited, on formal grounds, that the calculations of the exact critical points of the bond percolation and Ising models through the use of duality and star-triangle transformations can be unified within an appropriate graph framework. (Atomindex citation 14:803521)