Phase diagram of step faceting for sticky steps

A phase diagram for the step faceting phase, the step droplet phase, and the Gruber-Mullins-Pokrovsky-Talapov (GMPT) phase on a crystal surface is obtained by calculating the surface tension with the density matrix renormalization group method. The model based on the calculations is the restricted solid-on-solid (RSOS) model with a point-contact-type step-step attraction (p-RSOS model) on a square lattice. The point-contact-type step-step attraction represents the energy gain obtained by forming a bonding state with orbital overlap at the meeting point of the neighbouring steps. Owing to the sticky character of steps, there are two phase transition temperatures, $T_{f,1}$ and $T_{f,2}$. At temperatures $T<T_{f,1}$, the anisotropic surface tension has a disconnected shape around the (111) surface. At $T<T_{f,2}<T_{f,1}$, the surface tension has a disconnected shape around the (001) surface. On the (001) facet edge in the step droplet phase, the shape exponent normal to the mean step running direction ${\theta }_n=2$ at $T$ near $T_{f,2}$, which is different from the GMPT universal value ${\theta }_n=3\mathrm{/}2$. On the (111) facet edge, ${\theta }_n=4\mathrm{/}3$ only on $T_{f,1}$. To understand how the system undergoes phase transition, we focus on the connection between the p-RSOS model and the one-dimensional spinless quasi-impenetrable attractive bosons at absolute zero.