  A non-hermitian deformation of the one-dimensional transverse Ising model is
shown to have the property of quasi-hermiticity. The transverse Ising chain is
obtained from the starting non-hermitian Hamiltonian through a similarity
transformation. Consequently, both the models have identical eigen-spectra,
although the eigen-functions are different. The metric in the Hilbert space,
which makes the non-hermitian model unitary and ensures the completeness of
states, has been constructed explicitly. Although the longitudinal correlation
functions are identical for both the non-hermitian and the hermitian Ising
models, the difference shows up in the transverse correlation functions, which
have been calculated explicitly and are not always real. A proper set of
hermitian spin operators in the Hilbert space of the non-hermitian Hamiltonian
has been identified, in terms of which all the correlation functions of the
non-hermitian Hamiltonian become real and identical to that of the standard
transverse Ising model. Comments on the quantum phase transitions in the
non-hermitian model have been made.
