LAUSR

We show that the coefficients of the Hamiltonian for the $O(N)$ symmetric $\phi^4$ field theory in $N=1$ limit, may be expressed in terms of the known properties of the reference (hard-core) system: the compressibility and its derivatives with respect to density. We consider the fluid Hamiltonian with microscopic expressions for its coefficients when it is taken in the approximation up to second order of interaction term i.e. in the form of Landau-Ginzburg-Wilson Hamiltonian and explicitly demonstrate that it is equivalent to the Hamiltonian of the $\phi^4$ field theory model. We propose a rigorous generalization of known results for the critical interfacial tension to the microscopic case. Based on the renormalization group approach the analytical microscopic expression for the surface tension of liquids near the critical point is obtained which is in a good agreement with numerical experiments.