Equilibrium shape of $\rm ^4He$ crystal surfaces near critical orientations

Conditions for applying mean field theory to the thermodynamics of the $\rm ^4He$ 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.