Percolation transition in two-dimensional ±J Ising spin glasses

Conjectured exact percolation thresholds of the Fortuin–Kasteleyn cluster for the ±J Ising spin glass model

“…This result agrees with the previous results for T F K in Ref. [24]. This result does not contradict with the previous result for T D in Ref.…”

“…This is the result for the triangular lattice. The previous numerical results are T F K = 2.74(3) and 2.73(4) [24] for p = 0.6, and T F K = 2.75(3) and 2.76(3) [24] for p = 0.7. This result agrees with the previous results for T F K in Ref.…”

“…T F K does not agree with T C in this case. The previous numerical results are T F K = 1.81(2) and 1.82(3) [24] for p = 0.7, T F K = 1.83(2) and 1.83(3) [24] for p = 0.8, T D ∼ 1.8 [11] for p = 1/2, T D ∼ 1.70 [23] for p = 1/2, and T D = 1.69(2) [30] for p = 1/2. This result agrees with the previous results for T F K in Ref.…”

Fortuin-Kasteleyn and damage-spreading transitions in random-bond Ising lattices

“…Other parameters can still show finite size scaling deviations [34]. The large size limits for T F K (p) and T F Kr (p) remain equal to each other to within the numerical precision of the T F K (p) points [25] over the strong disorder range of p extending from p = 1/2 to p N L,F K in the square lattice, and from p ∼ 0.3 to p N L,F K in the triangular lattice. Over these ranges of p the satisfied bonds at T F K are very close to being uncorrelated; for instance at p = 1/2 on the square lattice −U (p, β F Kr )/ tanh(β F Kr ) = 0.9709 which remains near to the uncorrelated value of 1.…”

“…[23,24]. Imaoka et al [25] estimated T F K (p) numerically over the entire range of p for the square and triangular RBIM lattices.…”