Laplacian roughening models and two-dimensional melting

Roughening models which mimic the translational and rotational symmetries involved in two-dimensional melting are defined. One of the models is related via a duality transformation to a gas of disclinations in a solid interacting with an r²lnr potential. The theory of dislocation-mediated melting suggests a sequence of two continuous phase transitions for this gas and for the corresponding roughening models. Grain-boundary-mediated transitions are also possible. The roughening models are particularly amenable to computer simulations.