Commensurate melting, domain walls, and dislocations

Commensurate phases of order $p\ge 3$ 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 $3\times 1$ and $\sqrt{3}\times \sqrt{3}$ 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 $p\times 1$ 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 $d=2\mathrm{}$ the crossover exponent for dislocations is found to be ${-\theta }_p=\frac{(6-p^2)}{4}$. For $p>\mathrm{}\sqrt{6}$ 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 $d=2\mathrm{}$, $p=3\mathrm{}$, illustrating how a Lifshitz point may be present at all nonzero fugacities.