The behaviour of the many-body correlation functions in the vicinity of the liquid-gas critical point is investigated. The critical point is assumed to exist and is therefore introduced by the means of a phenomenological equation of state. We use only the framework of the liquid-state physics and thus no reference to an effective Landau-Ginzburg hamiltonian is made. From the relations linking the total correlation functions h^{(n)} and h^{(n+1)}, we show that the integrals of all the h^{(n)} diverge at the critical point. We then find that the GKS inequalities are satisfied under the condition that all the distances between the particles are asymptotically large. The range of validity of these inequalities in terms of interparticle distances is given and a particular attention must be paid to the fact that usual asymptotic approximations of the liquid state theory are no more valid.Comments: Refs. 13, Figs. 0, Tabs. 0.
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