Abstract
It has been recently established that heterogeneous bootstrap percolation and
related dynamic facilitation models exhibit a complex hierarchy of continuous
and discontinuous transitions depending on lattice connectivity and kinetic
constraints. Here the range of the previously observed phase diagram topologies
and higher-order singularities is extended to disconnected glass-glass
transitions and swallowtail bifurcations (generic and degenerate). The phase
diagram and the order parameter for two different types of spin mixtures are
analytically determined and an experimental realization of the new predictions
emerging in our approach is suggested.
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