Multi-particle critical correlations

Abstract

We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to the $k$-particle ones and their derivatives with respect to the density. Critical exponents corresponding to generalized compressibility equations resulting from the hierarchy are shown to grow linearly with the order of correlations. We prove that the critical behaviour requires taking into account correlation functions of arbitrary order. It is however only a necessary condition. Indeed, approximate closures of the hierarchy obtained by expressing higher order correlations in terms of lower order ones (Kirkwood's superposition approximation and its generalizations) turn out to be inconsistent with the critical behaviour.Comment: 14 pages, 1 figure; v2: minor change

Form invariance of the moment sum-rules for jellium with the addition of short-range terms in the pair-potential

“…Even if, as pointed out in Ref. [14], from the work of Santos and Piasecki [15] follows that the Ursell functions of any order are likely to have a long-range behavior on a critical point, thus violating our exponential clustering working-hypothesis.…”

“…the decay to zero of the truncated correlations faster than any inverse power of distance as groups of particles are separated by an infinite distance. In fact, it has to be expected that at criticality the correlation functions develops long-range tails with monotonous or oscillating inverse power law decay [15].…”