Supplementary Material

The Supplementary Material includes: the comparison of results obtained with the Nose'-Hoover thermostat with different time constants (Fig. S1); the comparison of results obtained with the Nose'-Hoover and Langevin thermostats (Figs. S2 and S3); the comparison of results obtained with the Nose'-Hoover and CSVR thermostats (Figs. S4 and S5); the initial and the final structures in a recrystallization simulation at 260 K for the basal and prism1 surfaces (Fig. S6); the time-evolution of the excess number of liquid-like molecules Delta n_l during the TIP4P/Ice and mW crystallization simulations for one replica at each temperature, for the basal and prism1 surfaces (Fig. S7); the piecewise linear fitting of the time-evolution of Delta n_l during the TIP4P/Ice crystallization simulations for the replicas of the ice Ih basal and prism1 surfaces from 240 K to 270 K (Fig. S8-S14); the time-evolution of the formation of the four ice bilayers above the interface where the melted area initially met the crystalline region for the basal and prism1 faces during the TIP4P/Ice crystallization process at 265 K (Fig. S15).