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

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... 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 θ_n=2 at T near T_f,2, which is different from the GMPT universal value θ_n=3/2. On the (111) facet edge, θ_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.