Shift exponent and breakdown of universality for the two-layer Ising model on a square lattice

By using a β-function for a spin-32 Ising model, we investigate the critical phenomena of a general two-layer Ising model of square lattice. We find that the value of the shift exponent ψ is 1.73 ± 0.04 for the system with the same intra-layer interaction and 0.5 for the system with different intra-layer interactions. We also find an evidence that the value of critical exponent ν exceeds 1 in some region of interaction-parameter space, where the degeneracy of the ground state is fourfold.