Decay of Correlations in Linear Systems

Abstract

The conditions under which the decay of the pair correlation function at large distances is monotonic or oscillatory are investigated for one-dimensional systems and discussed in detail for certain linear continuum and lattice models in which the molecules interact only with their nearest neighbors. In each case a locus is found in the pressure–temperature plane and in the density–temperature plane, such that in thermodynamic states of the one-dimensional fluid that lie on one side of the locus, the decay of the correlation function is oscillatory, and in those that lie on the other side it is monotonic. At every temperature the decay is monotonic below a uniquely determined transition pressure or density. It is argued that such loci will likewise be found in real three-dimensional systems, and that the critical point and a range of fluid states around the critical point, as well as states of the low-pressure vapor, will lie in the region in which the correlation function at large distances is asymptotically positive and decays monotonically.