∊-expansion of the surface tension in an external field

A system near criticality is considered in a linearly varying potential. With the order parameter profile, whether induced by the field ( T > T_c) or spontaneously formed ( T< T_c), a surface tension can be associated as the difference of the actual free energy and a reference free energy. The reference free energy is taken as that of a locally homogeneous system withvarying field strength, which leads to a convergent ε-expansion for the surface tension. This surface tension is a universal function of temperature and field strength and is evaluated to first order in ε.