  Strong magnetization in accretion discs could resolve a number of outstanding
issues related to stability and state transitions in low-mass X-ray binaries.
However, it is unclear how real discs become strongly magnetized and, even if
they do, whether they can remain in such a state. In this paper, we address the
latter issue through a pair of global disc simulations. Here, we only consider
cases of initially purely toroidal magnetic fields contained entirely within a
compact torus. We find that, over only a few tens of orbital periods, the
magnetization of an initially strongly magnetized disc,
$P_\mathrm{mag}/P_\mathrm{gas} \ge 10$, drops to $\lesssim 0.1$, similar to the
steady-state value reached in initially weakly magnetized discs. This is
consistent with recent shearing box simulations with initially strong toroidal
fields, the robust conclusion being that strongly magnetized toroidal fields
can not be locally self-sustaining. These results appear to leave net poloidal
flux or extended radial fields as the only avenues for establishing strongly
magnetized discs, ruling out the thermal collapse scenario.
