  A quantum computer based on Majorana qubits would contain a large number of
zero-energy Majorana states. This system can be modelled as a connected network
of the Ising-Kitaev chains alternating the "trivial" and "topological" regions,
with the zero-energy Majorana fermions localized at their interfaces. The
low-energy sector of the theory describing such a network can be formulated in
terms of leading-order couplings between the Majorana zero modes. I consider a
minimal model exhibiting effective couplings between four Majorana zero modes -
the nonuniform Ising-Kitaev chain, containing two "topological" regions
separated by a "trivial" region. Solving the model exactly, I show that for
generic values of the model parameters the four zero modes are localized at the
four interface points of the chain. In the special case where additional
inversion symmetry is present, the Majorana zero modes are "delocalized"
between two interface points. In both cases, the low-energy sector of the
theory can be formulated in terms of the localized Majorana fermions, but the
couplings between some of them are independent of their respective separations:
the exact solution does not support the "nearest-neighbor" form of the
effective low-energy Hamiltonian.
