Commensurate melting, domain walls, and dislocations

Commensurate phases of order p3 exhibit two or more classes of inequivalent domain walls, reflecting a lower than ideal symmetry. These walls compete statistically and undergo wetting transitions. New "chiral" universality classes of melting transitions may thereby occur for both 31 and 33 surface phases. The data of Moncton et al. may be interpreted as indicating that such a chiral transition occurs in Kr on graphite. The melting of p1 phases is discussed for various dimensionalities d and values of p. Domain-wall wetting transitions are treated in a semiphenomenological fashion; they may be either continuous or first order. Wetting critical exponents are obtained for a general class of transitions. The role of dislocations at the uniaxial commensurate-to-incommensurate transition is examined. For d=2 the crossover exponent for dislocations is found to be -₏= (6-{p^2) }4. For p>6 the dislocations are therefore irrelevant, but they introduce singular corrections to scaling at the transition. A phase diagram as a function of dislocation fugacity is proposed for the case d=2, p=3, illustrating how a Lifshitz point may be present at all nonzero fugacities.