  We propose that the Higgs phase of a gauge Higgs theory is the phase of
spontaneously broken custodial symmetry, and present a new gauge invariant
order parameter for custodial symmetry breaking which is very closely analogous
to the Edwards-Anderson order parameter for spin glasses. Custodial symmetry is
a global symmetry acting on the Higgs field alone, and we show here that the
spin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgs
phase of broken custodial symmetry, coincides with the transition between two
distinct types of confinement. These are color confinement in the Higgs phase,
and a stronger version of confinement, which we have termed
"separation-of-charge" confinement, in the QCD-like phase.
