  We have introduced a novel Majorana representation of S=1/2 spins using the
Jordan-Wigner transformation and have shown that a generalized spin model of
Kitaev defined on a brick-wall lattice is equivalent to a model of
non-interacting Majorana fermions with Z_2 gauge fields without redundant
degrees of freedom. The quantum phase transitions of the system at zero
temperature are found to be of topological type and can be characterized by
nonlocal string order parameters. In appropriate dual representations, these
string order parameters become local order parameters and the basic concept of
Landau theory of continuous phase transition can be applied.
