Multicomponent Order Parameter for Surface Melting

Abstract

A multicomponent order parameter for surface melting is introduced which depends both on the structure of the bulk crystal and on the orientation of the crystal surface. Each order-parameter component, $\tilde{M}\left({\mathrm{Q}}^{\parallel }\right)$, corresponds to a reciprocal-lattice vector, ${\mathrm{Q}}^{\parallel }$, of the two-dimensional lattice parallel to the surface. For complete surface melting, all order-parameter components with $\left|{\mathrm{Q}}^{\parallel }\right|$ vanish simultaneously but the associated critical behavior depends on the length of ${\mathrm{Q}}^{\parallel }:\tilde{M}\left({\mathrm{Q}}_i^{\parallel }\right)$ vanishes faster than $\tilde{M}\left({\mathrm{Q}}_j^{\parallel }\right)$ if $\left|{\mathrm{Q}}_i^{\parallel }\mathrm{}\right|>\mathrm{}\left|\mathrm{}{\mathrm{Q}}_j^{\parallel }\right|$. For a surface of low symmetry, this implies a marked anisotropy of the melting process.