$\phi^4$ Theory Hamiltonian for Fluids: Application to the surface tension near the critical point

We show that the surface tension of fluid near the critical point may be correctly described by taking into consideration the microscopic structure of the system using a {\phi}4 field theory. We revise the theory of the surface tension near criticality to take into account a microscopic structure of the fluid. Focusing on the case of the Lennard-Jones fluid, we express the surface tension in terms of the compressibility of the reference hard-core system and its derivatives with respect to density. We demonstrate that the obtained analytical microscopic expression for the surface tension near the critical point is in a good agreement with numerical experiments, which emphasizes the impact of microscopic structure on the critical behavior of the surface tension in fluids. Our analysis provides a basis for studying the surface tension in small-volume systems important in many technological applications.