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We study the ground-state properties of a spin-1/2 model on a chaincontaining four-spin Ising-like interactions in the presence of both transverseand longitudinal magnetic fields. We use entanglement entropy and finite-sizescaling methods to obtain the phase diagrams of the model. Our numericalcalculations reveal a rich variety of phases and the existence ofmulti-critical points in the system. We identify phases with both ferromagneticand anti-ferromagnetic orderings. We also find periodically modulated orderingsformed by a cluster of like-spins followed by another cluster of oppositelike-spins. The quantum phases in the model are found to be separated by eitherfirst or second order transition lines.

Critical behavior of a quantum chain with four-spin interactions in the presence of longitudinal and transverse magnetic fields