Density-matrix renormalization-group study for a two-dimensional lattice-gas on the Ih-ice prism surface

The phase transition temperature of a two-dimensional (2D) lattice-gas model for the Ih-ice prism surface ((1010) surface on a wurtzite crystal structure) is calculated using the density-matrix renormalization-group (DMRG) method. Since the unit cell on the prism surface contains four atoms without inversion symmetry, the asymmetric version of the DMRG is required to obtain a precise value of the phase transition temperature. The effective bond energy on the surface is obtained by comparing the phase transition temperature with the faceting transition temperature observed for a real ice crystal. Using the effective bond energy, the temperature dependence of the coverage on sub-lattice sites is calculated. The surface tensions on the (0001) surface (the basal plane) and the prism plane are also calculated. The surface tension of the basal plane for the ice/water interface agrees well with the recent calculated values obtained by large scale molecular dynamics.