  The surface tension of rough interfaces between coexisting phases in 2D and
3D Ising models are discussed in view of the known results and some original
calculations presented in this paper. The results are summarised in a formula,
which allows to interpolate the corrections to finite-size scaling between two
and three dimensions. The physical meaning of an analytic continuation to
noninteger values of the spatial dimensionality d is discussed. Lattices and
interfaces with properly defined fractal dimensions should fulfil certain
requirements to possibly have properties of an analytic continuation from
d-dimensional hypercubes. Here 2 appears as the marginal value of d below which
the (d-1)-dimensional interface splits in disconnected pieces. Some
phenomenological arguments are proposed to describe such interfaces. They show
that the character of the interfacial fluctuations at d<2 is not the same as
provided by a formal analytic continuation from d-dimensional hypercubes with d
>= 2. It, probably, is true also for the related critical exponents.
