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 × 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.