  We study the finite temperature and magnetic field phase diagram of electrons
on the pyrochlore lattice subject to a local repulsion as a model for the
pyrochlore iridates. We provide the most general symmetry-allowed Hamiltonian,
including next-nearest neighbour hopping, and relate it to a Slater-Koster
based Hamiltonian for the iridates. It captures Lifshitz and/or thermal
transitions between several phases such as metals, semimetals, topological
insulators and Weyl semimetals, and gapped antiferromagnets with different
orders. Our results on the charge conductivity, both DC and optical, Hall
coefficient, magnetization and susceptibility show good agreement with recent
experiments and provide new predictions. As such, our effective model sheds
light on the pyrochlore iridates in a unified way.
