Entropy of hexagonal ice monolayer and of other three-coordinated systems

To calculate the entropy of three-coordinated ice-like systems, a simple and convenient approximate method of local conditional transfer matrices using 2 x 2 matrices is presented. The exponential rate of convergence of the method has been established, which makes it possible to obtain almost exact values of the entropy of infinite systems. The qualitatively higher rate of convergence for three-coordinated systems compared to four-coordinated systems is due to less rigid topological restrictions on the direction of hydrogen (H-) bonds in each lattice site, which results in a significantly weaker the system's total correlations. Along with the ice hexagonal monolayer, other three-coordinated lattices obtained by decorating a hexagonal monolayer, a square lattice, and a kagome lattice were analyzed. It is shown that approximate cluster methods for estimating the entropy of infinite three-coordinated systems are also quite accurate. The importance of the proposed method of local conditional transfer matrices for ice nanostructures is noted, for which the method is exact.