Renormalization Group Approach to the Interfacial Order Parameter Profile near the Critical Point

Abstract

The interfacial order parameter profile near the criticfal point is studied using the renormalization group method. The equation for the order parameter profile is derived up to first order in ε= 4 - d where d is the spatial dimensionality of the system. This equation consists of two parts. One is related to the equation of state with a slight modification. The other comes from the spatial inhomogeneity of the order parameter. Our result is compared with that of Fisk and Widom in which the form of the equation of state has been postulated. An explicit solution of the equation which describes the order parameter profile is obtained. The universal amplitude of the surface tension is also evaluated using the ε-expansion technique.