Microcanonical determination of the order parameter critical exponent

Abstract

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 ${\beta }_{\epsilon }$, thus demonstrating that critical exponents can be determined by analysing directly the density of states of finite systems.

5 pages, 3 figures included, to appear in Int. J. Mod. Phys. C

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