  We present a toy model with a Hamiltonian $H^{(2)}_T$ on a folded
one-dimensional spin chain. The non-trivial ground states of $H^{(2)}_T$ are
separated by a gap from the excited states. By analyzing the symmetries in the
model, we find that the topological order is protected by a $\mathbb{Z}_2$
global symmetry. However, by using perturbation series and excluding thermal
effects, we show that the $\mathbb{Z}_2$ symmetry is stable in comparison to a
standard nearest-neighbor Ising model with a Hamiltonian $H_I$. We find that
$H^{(2)}_T$ is a member of a family of Hamiltonians that are adiabatically
connected to $H_I$. Furthermore, the generalizations of this class of
Hamiltonians, their adiabatic connection to $H_I$, and the relation to quantum
error-correcting codes are discussed. Finally, we show the correspondence
between the two ground states of $H^{(2)}_T$ and the unpaired Majorana modes,
and provide numerical examples.
