  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 $\theta_n=3/2$. On the (111) facet edge,
$\theta_n=4/3$ 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.
