Microcanonical determination of the order parameter critical exponent

A highly efficient Monte Carlo method for the calculation of the density of states of classical spin systems is presented. As an application, we investigate the density of states Omega(N) (E, M) of two- and three-dimensional Ising models with N spins as a function of energy E and magnetization M. For a fixed energy lower than a critical value EcN the density of states exhibits two sharp maxima at M = +/-M-sp(E) which define the microcanonical spontaneous magnetization. An analysis of the form M-sp(E) proportional to (E-c,E-infinity - E)(betaepsilon) yields very good results for the critical exponent beta(epsilon) thus demonstrating that critical exponents can be determined by analyzing directly the density of states of finite systems.