Melting transition of a network model in two dimensions

Abstract:

The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths.