Comparison of 2D melting criteria in a colloidal system.

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as the hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal-hexatic and hexatic-isotropic liquid phase transitions for the same experimental data of the given setup. The criteria are the bond orientational correlation function, the Larson-Grier criterion, the 2D dynamic Lindemann parameter, the bond orientational susceptibility, the 2D Hansen-Verlet rule, the Löwen-Palberg-Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long-range repulsion, the bond order correlation function and bond order susceptibility work best to identify the hexatic-isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic-crystalline transition.