  We present a comprehensive study of a three-orbital lattice model suitable
for the layered iridate Sr2IrO4. Our analysis includes various on-site
interactions (including Hubbard and Hund's) as well as compressive strain, and
a Zeeman magnetic field. We use a self-consistent mean field approach with
multiple order parameters to characterize the resulting phases. While in some
parameter regimes the compound is well described by an effective J=1/2 model,
in other regimes the full multiorbital description is needed. As a function of
the compressive strain, we uncover two quantum phase transitions: first a
continuous metal-insulator transition, and subsequently a first order magnetic
melting of the antiferromagnetic order. Crucially, bands of both J=1/2 and
J=3/2 nature play important roles in these transitions. Our results
qualitatively agree with experiments of Sr2IrO4 under strain induced by a
substrate, and motivate the study of higher strains.
