Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions

We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, w≤20, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite w are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudocritical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, ν (2d). We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the w dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: ν (2d) =1.25 (8), x (2d) =0.996 (15), and ψ (2d) =0.51 (3).