  A phase diagram is a graph in parameter space showing the phase boundaries of
a many-particle system. Commonly, the control parameters are chosen to be those
of the (generalized) canonical ensemble, such as temperature and magnetic
field. However, depending on the physical situation of interest, the
(generalized) microcanonical ensemble may be more appropriate, with the
corresponding control parameters being energy and magnetization. We show that
the phase diagram on this parameter space looks remarkably different from the
canonical one. The general features of such a microcanonical phase diagram are
investigated by studying two models of ferromagnets with short-range
interactions. The physical consequences of the findings are discussed,
including possible applications to nuclear fragmentation, adatoms on surfaces,
and cold atoms in optical lattices.
