PROPERTIES OF THE N-BODY CORRELATION-FUNCTIONS NEAR THE LIQUID-GAS CRITICAL-POINT, CORRELATION INEQUALITIES

We investigate the behavior of the many-body correlation functions in the vicinity of the gas-liquid critical point. We use the framework of the liquid state theory and, accordingly, no reference to an effectiv e Landau-Ginzburg Hamiltonian is made. The critical condition is intro duced by means of the equation of state. From the Baxter equation rela ting the many-body correlation functions h(n) and h(n + 1), we find th at the integrals of all the h(n) diverge at the critical point. Then w e present strong arguments and this leads to GKS-like inequalities, un der some limiting conditions: the interparticle distances must be larg e and the thermodynamic state of the system must be close to the criti cal point. In order to get these inequalities, an upper bound for h(n) is obtained. Particular attention must be paid to the fact that the u sual asymptotic approximations of the liquid state theory are no longe r valid.