  A new microcanonical equilibrium state is introduced for quantum systems with
finite-dimensional state spaces. Equilibrium is characterised by a uniform
distribution on a level surface of the expectation value of the Hamiltonian.
The distinguishing feature of the proposed equilibrium state is that the
corresponding density of states is a continuous function of the energy, and
hence thermodynamic functions are well defined for finite quantum systems. The
density of states, however, is not in general an analytic function. It is
demonstrated that generic quantum systems therefore exhibit second-order
(continuous) phase transitions at finite temperatures.
