  By means of the principle of minimal sensitivity we generalize the
microcanonical inflection-point analysis method by probing derivatives of the
microcanonical entropy for signals of transitions in complex systems. A
strategy of systematically identifying and locating independent and dependent
phase transitions of any order is proposed. The power of the generalized method
is demonstrated in applications to the ferromagnetic Ising model and a
coarse-grained model for polymer adsorption onto a substrate. The results shed
new light on the intrinsic phase structure of systems with cooperative
behavior.
