Equilibrium shape of He-4 crystal surfaces near critical orientations

Conditions for applying mean field theory to the thermodynamics of the He-4 crystal surface are determined. Although the faceting transition itself is of the Berezinskii-Kosterlitz-Thouless type, the thermodynamic potential outside a narrow neighborhood of the transition temperature can be expanded in the spirit of the Landau theory of second-order phase transitions. A Ginzburg-Levanyuk parameter is found. The singular behavior of the surface stiffness near critical directions observed for essentially noncritical temperatures is explained.