Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach

The critical point (K_c) of the two-layer Ising model on the Kagome lattice has been calculated with a high precision, using the probabilistic cellular automata with the Glauber algorithm. The critical point is calculated for different values of the inter- and intra-layer couplings (K₁≠K₂≠K₃≠K_z), where K₁, K₂ and K₃ are the nearest-neighbor interactions within each layer in the 1, 2 and 3 directions, respectively, and K_z is the intralayer coupling. A general ansatz equation for the critical point is given as a function of the inter- and intra-layer interactions, ξ=K₃/K₁,σ=K₂/K₁ and ω=K_z/K₁ for the one- and two-layer Ising models on the Kagome lattice.