Microcanonical determination of the order parameter critical exponent

Details Microcanonical determination of the order parameter critical exponent Microcanonical determination of the order parameter critical exponent

2001-10-04

arxiv.org/abs/cond-mat/0110090v2

Int. J. Mod. Phys. C 13, 947-956 (2002)

Physics

Condensed Matter

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

Scientific paper

10.1142/S0129183102003693

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.

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