Critical phenomena in liquids (theory)

It is shown that the Ornstein-Zernike equation has two solutions, classic (analytic) and critical (not analytic). Closure equations of the HNC, PY, etc. types well known in the theory of liquids correspond to the first solution. The second solution presupposes that the bridge functional of a system has the form of the sum B = B ^rg + B ^cr, where B ^rg is a regular (analytic) function of density and B ^cr is a critical (not analytic) function. It is shown the classic solution determines the coordinates of the critical point, critical amplitudes, and the other parameters of critical phenomena depending on the individual liquid characteristics. The critical solution determines the critical indices and the equations relating them. The regions in which classic and critical solutions are valid are separated on the phase plane by a line of singular points, at which the second derivatives of pressure experience discontinuity.