On the nature of the contributions to the entropy of Pauling ice

Abstract

A calculation is presented for the entropy and correlation functions of Pauling ice - a model in which the energy of the microstates can take only two values: zero or infinity. The central point of the proposed approach is the use of a canonical expansion of the thermodynamic functions in irreducible multiparticle correlations. Reduction rules are formulated which establish the relation between the correlation functions of orders 1, ...,k-1 and the kth-order correlation function of the system. The latter is calculated on the basis of the assumption of equal probabilities of all allowed configurations of a compact group of k particles and the normalization condition. The order of approximation is determined by the number of particles k for which the correlations between states is taken into account. It is shown that with increasing k the values of the entropy of two-dimensional "square ice" converge nonmonotonically to its exact value obtained by Lieb. The best agreement corresponds to those approximations in which the group of k particles has the lattice symmetry and contains closed loops of hydrogen bonds. The method can be extended to arbitrary lattice systems. © 2003 American Institute of Physics.