  The accurate determination of magnetic phase transitions in electronic
systems is an important task of solid state theory. While numerically exact
results are readily available for model systems such as the half-filled 3D
Hubbard model, the complexity of real materials requires additional
approximations, such as the restriction to certain classes of diagrams in
perturbation theory, that reduce the precision with which magnetic properties
are described. In this work, we examine the description of magnetic properties
in second order perturbation theory, GW, FLEX, and two TMatrix approximations
to numerically exact CT-QMC reference data. We assess finite-size effects and
compare periodic lattice simulations to cluster embedding. We find that
embedding substantially improves finite size convergence. However, by analyzing
different partial summation methods we find no systematic improvement in the
description of magnetic properties, with most methods considered in this work
predicting first-order instead of continuous transitions, leading us to the
conclusion that non-perturbative methods are necessary for the accurate
determination of magnetic properties and phase transitions.
