  We study the onset of eigenstate thermalization in the two-dimensional
transverse field Ising model (2D-TFIM) in the square lattice. We consider two
non-equivalent Hamiltonians: the ferromagnetic 2D-TFIM and the
antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We
use full exact diagonalization to examine the behavior of quantum chaos
indicators and of the diagonal matrix elements of operators of interest in the
eigenstates of the Hamiltonian. A finite size scaling analysis reveals that
quantum chaos and eigenstate thermalization occur in those systems whenever the
fields are nonvanishing and not too large.
