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 E_{c,N} the density of states exhibits two sharp maxima at $M=\pm M_{sp}(E)$ which define the microcanonical spontaneous magnetization. An analysis of the form $M_{sp}(E) \propto (E_{c,\infty}-E)^{\beta_\epsilon}$ yields very good results for the critical exponent ${\beta }_{ϵ}$, thus demonstrating that critical exponents can be determined by analysing directly the density of states of finite systems.