  Motivated by the duality between site-centered spin and bond-centered spin in
one-dimensional system, which connects two different constructions of fermions
from the same set of Majorana fermions, we show that two-dimensional models
with topological orders can be constructed from certain well-known models with
classical orders characterized by symmetry-breaking. Topology-dependent ground
state degeneracy, vanishing two-point correlation functions, and unpaired
Majorana fermions on boundaries emerge naturally from such construction. The
approach opens a new way to construct and characterize topological orders.
