  We study fermion-parity-changing quantum phase transitions (QPTs) in platform
Josephson junctions. These QPTs, associated with zero-energy bound states, are
rather widely observed experimentally. They emerge from numerical calculations
frequently without detailed microscopic insight. Importantly, they may
incorrectly lend support to claims for the observations of Majorana zero modes.
In this paper we present a fully consistent solution of the Bogoliubov-de
Gennes equations for a multi-component Josephson junction. This provides
insights into the origin of the QPTs. It also makes it possible to assess the
standard self energy approximations which are widely used to understand
proximity coupling in topological systems. The junctions we consider are
complex and chosen to mirror experiments. Our full proximity calculations
associate the mechanism behind the QPT as deriving from a spatially extended,
proximity-induced magnetic "defect". This defect arises because of the
insulating region which effects a local reorganization of the bulk
magnetization in the proximitized superconductor. Our results suggest more
generally that QPTs in Josephson junctions generally do not require the
existence of spin-orbit coupling and should not be confused with, nor are they
indicators of, Majorana physics.
