Non-equilibrium Relaxation Analysis on Two-dimensional Melting

The melting transition in the hard-disk system is considered. Non-equilibrium relaxation analysis of the six-fold bond-orientational order parameter has been carried out. The critical point between the hexatic and the fluid phase is determined on the basis of the dynamic scaling hypothesis. The value of the critical exponent $\eta$ is determined from the fluctuation of the order parameter at the criticality as $\eta = 0.25(2)$ which is consistent with the prediction by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.