  Canonical analysis has long been the primary analysis method for studies of
phase transitions. However, this approach is not sensitive enough if transition
signals are too close in temperature space. The recently introduced generalized
microcanonical inflection-point analysis method not only enables the systematic
identification and classification of transitions in systems of any size, but it
can also distinguish transitions that standard canonical analysis cannot
resolve. By applying this method to a generic coarse-grained model for
semiflexible polymers, we identify a mixed structural phase dominated by
secondary structures such as hairpins and loops that originates from a
bifurcation in the hyperspace spanned by inverse temperature and bending
stiffness. This intermediate phase, which is embraced by the well-known
random-coil and toroidal phases, is testimony to the necessity of balancing
entropic variability and energetic stability in functional macromolecules under
physiological conditions.
