  The critical properties of the one-dimensional transverse Ising model in the
presence of a longitudinal magnetic field were studied by the quantum fidelity
method. We used exact diagonalization to obtain the ground-state energies and
corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the
fidelity susceptibility is used to locate the various phase boundaries present
in the system. The type of dominant spin ordering for each phase was identified
by examining the corresponding ground-state eigenvector. For a given
antiferromagnetic nearest-neighbor interaction J2, we calculated the fidelity
susceptibility as a function of the transverse field (Bx) and the strength of
the longitudinal field (Bz). The phase diagram in the (Bx,Bz)-plane shows three
phases. These findings are in contrast with the published literature that
claims that the system has only two phases. For Bx < 1, we observed an
antiferromagnetic phase for small values of Bz and a paramagnetic phase for
large values of Bz. For Bx > 1 and low Bz, we found a disordered phase that
undergoes a phase transition to a paramagnetic phase for large values of Bz.
