Properties of the H-bond network for two-dimensional lattice water model

A microscopic Hamiltonian of the hydrogen-bond network in two-dimensional lattice water is proposed, which describes the formation and disruption of the H bonds, their bending, and which satisfies the Bernal-Fowler rules [J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]. The thermodynamic properties of the H-bond network are studied using the method of many-particle irreducible distribution functions, which is a generalization of the Kikuchi cluster approach [R. Kikuchi, Phys. Rev. 81, 988 (1951)] and the Bethe-Peierls quasiactivities method [H. A. Bethe, Prog. R. Soc. A 150, 552 (1935)]. The temperature dependencies of the average number of H bonds per molecules, the contribution of the H bonds into the heat capacity of the system, and the parameters describing the correlations between the states of molecules on the neighboring sites are investigated. It is shown that depending on the magnitude of the interaction between the H bonds in the H-bond subsystem either smooth or sharp first-order phase transition can occur. The role of different factors in the formation of the properties of the H-bond network is discussed.