  We study the ground-state properties of a spin-1/2 model on a chain
containing four-spin Ising-like interactions in the presence of both transverse
and longitudinal magnetic fields. We use entanglement entropy and finite-size
scaling methods to obtain the phase diagrams of the model. Our numerical
calculations reveal a rich variety of phases and the existence of
multi-critical points in the system. We identify phases with both ferromagnetic
and anti-ferromagnetic orderings. We also find periodically modulated orderings
formed by a cluster of like-spins followed by another cluster of opposite
like-spins. The quantum phases in the model are found to be separated by either
first or second order transition lines.
