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 ( K 1 ≠ K 2 ≠ K 3 ≠ K z ) , where K 1 , K 2 and K 3 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 = K 3 / K 1 , σ = K 2 / K 1 and ω = K z / K 1 for the one- and two-layer Ising models on the Kagome lattice.