  We investigate two concrete cases of phase transitions breaking a subsystem
symmetry. The models are two classical compass models featuring line-flip and
plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev
Hamiltonian on a cubic lattice. We show that these models experience a hybrid
symmetry breaking by which the system display distinct symmetry broken patterns
in different submanifolds. For instance, the system may look magnetic within a
chain or plane but nematic-like when observing from one dimensionality higher.
We fully characterize the symmetry-broken phases by a set of subdimensional
order parameters and confirm numerically both cases undergo a non-standard
first-order phase transition. Our results provide new insights into phase
transitions involving subsystem symmetries and generalize the notion of
conventional spontaneous symmetry breaking.
