Calculation of the critical exponents by a renormalization of the Ornstein-Zernike equation

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Abstract
We calculate the critical exponents at the liquid-vapor critical point by using the classical ingredients of the liquid-state theory. Two coupling constants are defined at a microscopic level. The closure of the Ornstein-Zernike equation is given by the Callan-Symanzik equation from which we determine the position of the fixed point. The role of the three-body direct-correlation function is emphasized. A comparison between this work and the standard theory of critical phenomena based on the Landau-Ginzburg-Wilson Hamiltonian is presented.