IMPOSSIBILITY OF OBSERVING A CONTINUOUS COMMENSURATE-INCOMMENSURATE TRANSITION

It has been shown previously [J. Lajzerowicz and A. P. Levanyuk, Phys. Rev. B 49, 15 475 (1994)] that in a perfect three-dimensional crystal the commensurate-incommensurate transition is always discontinuous du e to a fluctuation-induced long-range attraction between domain walls. At the same time it has been concluded long ago that in real crystals a strong repulsion between the domain walls exists due to impurity-in duced roughening of the domain walls. This poses the question whether the commensurate-incommensurate transition becomes continuous in real crystals. We argue that the most important point to answer this questi on is that a very slow activation motion of domain walls over disorder -induced potential barriers is necessary for making the repulsion oper ative, so that over a reasonable time of experiment this interaction ' 'propagates'' to distances that are no more than one order of magnitud e bigger than the domain-wall width. Meanwhile the attractive interact ions between the domain walls ''propagate'' almost instantaneously, th us leading to the conclusion that experimentally observed commensurate -incommensurate transition will always be discontinuous. Our estimates show that for structural incommensurate systems the ''equilibrium'' d istance between the domain walls near transition point has the same or der of magnitude as the domain-wall width.