Finite-size scaling in the transverse Ising model on a square lattice

Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6 x 6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming universality with the three-dimensional classical Ising model. Critical amplitudes are also estimated for both the energy gap and the ground-state energy.