Trimer-Monomer Mixture Problem on (111) 1×11 \times 1 Surface of Diamond Structure

We consider a system of trimers and monomers on the triangular lattice, which describes the adsorption problem on (111) $1 \times 1$ surface of diamond structure. We give a mapping to a 3-state vertex model on the square lattice. We treat the problem by the transfer-matrix method combined with the density-matrix algorithm, to obtain thermodynamic quantities.Comment: 9 pages, 7 figures, PTPTeX ver. 1.0. To appear Progress of Theoretical Physics, Jan. 2001. http://www2.yukawa.kyoto-u.ac.jp/~ptpwww/ (Full Access

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 $\theta_n=3/2$. 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.Comment: 26 pages, 15 figure

Profile of a Faceted Macrostep Caused by Anomalous Surface Tension

The height profile of a macrostep on a vicinal surface near equilibrium is studied numerically using a restricted solid-on-solid model with a point-contact-type step-step attraction (p-RSOS model). We calculate the surface tension of vicinal surfaces around the (001) surface inclined towards the 111 direction using the density-matrix-renormalization group method. We also calculate the height profiles of vicinal surfaces using the Monte Carlo method and study the connection between the height profile of the macrostep near equilibrium and the discontinuous surface tension. We find that the height profile of a macrostep on a vicinal surface near equilibrium can be classified depending on the zone in the faceting diagram where the system exists. We also find finite size effects both for the height profile and for the inhibition of the macrostep motion in the relaxation process to the equilibrium state

Statistical Mechanical Calculation of Anisotropic Step Stiffness of a Two-Dimensional Hexagonal Lattice Gas Model with Next-Nearest-Neighbor Interactions: Application to Si(111) Surface

We study a two-dimensional honeycomb lattice gas model with both nearest- and next-nearest-neighbor interactions in a staggered field, which describes the surface of stoichiometrically binary crystal. We calculate anisotropic step tension, step stiffness, and equilibrium island shape, by an extended random walk method. We apply the results to Si(111) 7$\times$7 reconstructed surface and high-temperature Si(111) 1$\times$1 surface. We also calculate inter-step interaction coefficient.Comment: revised on May 29 1999: RevTeX v3.1, 10 pages with 9 figures (one figure added

Non-universal equilibrium crystal shape results from sticky steps

The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) using the Monte Carlo method, where p=(dz/dx, dz/dy)$, and represents the thermal averag |p| dependence of , we derive a |p|-expanded expression for the non-universal surface free energy f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f_{eff}(p).Comment: 31 pages, 21 figure