Conditions for applicability of mean field theory to the thermodynamics of the ⁴He crystal surface are determined. Although the faceting transition itself is of Berezinsky—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. The Ginzburg—Levanyuk parameter is estimated. The singular behavior of the surface stiffness near critical directions observed for essentially non-critical temperatures is explained.

Keywords: quantum crystals, phase transitions, surface phenomena, Berezinsky—Kosterlitz—Thouless transitions PACS: 05.70.Np, 67.80.−s, 68.35.−p, 68.35.Rh (all) DOI: 10.3367/UFNe.2017.12.038352 URL: https://ufn.ru/en/articles/2018/11/g/ 000457154900007 2-s2.0-85062301877 2018PhyU...61.1090A Citation: Andreev A F, Melnikovsky L A "Equilibrium shape of 4He crystals near critical surface directions" Phys. Usp. 61 1090–1093 (2018) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 30th, March 2018, accepted: 13th, December 2017 Оригинал: Андреев А Ф, Мельниковский Л А «Равновесная форма поверхности кристаллов 4He вблизи критических ориентаций» УФН 188 1199–1202 (2018); DOI: 10.3367/UFNr.2017.12.038352