  The basic quantity for the description of the statistical properties of
physical systems is the density of states or equivalently the microcanonical
entropy. Macroscopic quantities of a system in equilibrium can be computed
directly from the entropy. Response functions such as the susceptibility are
for example related to the curvature of the entropy surface. Interestingly,
physical quantities in the microcanonical ensemble show characteristic
properties of phase transitions already in finite systems. In this paper we
investigate these characteristics for finite Ising systems. The singularities
in microcanonical quantities which announce a continuous phase transition in
the infinite system are characterised by classical critical exponents.
Estimates of the non-classical exponents which emerge only in the thermodynamic
limit can nevertheless be obtained by analyzing effective exponents or by
applying a microcanonical finite-size scaling theory. This is explicitly
demonstrated for two- and three-dimensional Ising systems.
