Physlca A 154 (1989) 511-520 North-Holland, Amsterdam CRITICAL POINTS CHARACTERIZATION USING PROBABILITY DISTRIBUTIONS II. PHASE TRANSITION OF LIQUID BINARY MIXTURES J GUI~MEZ, S VELASCO and A CALVO HERNANDEZ Departamento de Ffsma, Facultad de Clenctas, Umversldad de Salamanca, 37008 Salamanca, Spare Received 15 July 1988 A renormahzatlon-group-hke method, developed m a preceding paper, Js apphed to characterize critical points in hquld binary mixtures The method ~s based on the behavior of the probability distribution associated to these systems Two examples are developed In the first case (T-independent energy lnterachon between unhke molecules), the isomorphism wah the llqmd-gas phase transition is estabhshed In the second one (T-dependent energy lnterachon between unhke molecules), the difference between simple and double critical points appearing m closed-loop phase diagrams Is reported 1. Introduction In a preceding paper (hereafter referred to as paper I) a renormahzatton- group-hke method based on the use of probablhty distributions is applied to characterize the critical point and the coexistence line for the hqutd-gas phase transalon [1] In another recent paper [2] we have obtained the probablhty distribution for a binary hquld model from which different temperature vs composition phase diagrams can be reported In particular, closed-loop phase-diagrams [3] with upper (UCT) and lower (LCT) critical temperatures have been obtained Furthermore, analytic calculations have been carried out by assuming an explicit and simple T-dependence of the interaction energy between unhke molecules In the case that the closed loop reduces to a point, upper and lower crlttcal temperatures coincide and the critical point is a double critical point The present work is devoted to apply the method developed m paper I to hquld binary rnlxtures, in order to characterize the different critical points (single, upper and lower, double) appearing in these systems 0378-4371/89/$03 50 © Elsevier Science Publishers B V (North-Holland Physics Pubhshlng Division)