  We investigate a lattice version of the Yang-Lee model which is characterized
by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to
implement PT-symmetry on the lattice, which serves to guarantee the reality of
the spectrum in certain regions of values of the coupling constants. In that
region of unbroken PT-symmetry we construct a Dyson map, a metric operator and
find the Hermitian counterpart of the Hamiltonian for small values of the
number of sites, both exactly and perturbatively. Besides the standard
perturbation theory about the Hermitian part of the Hamiltonian, we also carry
out an expansion in the second coupling constant of the model. Our
constructions turns out to be unique with the sole assumption that the Dyson
map is Hermitian. Finally we compute the magnetization of the chain in the z
and x direction.
