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Equilibrium shape of 4He crystal surfaces near critical orientations

Conditions for applying mean field theory to the thermodynamics of the 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.