Interface Structures and Hamiltonians: Exact Results

There have been many recent applications of interface models and Hamiltonians to problems in the theory of wetting. These models help to understand more abstract calculations on the type of problem which can be treated on the one hand, and on the other, to extend the type of problem which can be treated. A very recent example of this is corner wetting, also known as filling. This contribution discusses the validity of such concepts from first principles using exactly calculated interface structures and phase diagrams. The planar Ising model, with boundary conditions and surface fields imposed to bring in wetting, is used. The well-known Jordan–Wigner transformation to lattice fermions is composed of a product of spin reversals to one side (on a strip) of the point at which the lattice Fermi operator acts. Such spin reversals introduce a domain wall in a natural way which can be exploited to bring in interface Hamiltonians in a natural and precise way. The perennial problem of intrinsic structure is discussed. The findings do not support the notion of such a structure attached to capillary waves by convolution. In a sense to be made precise, kinks have to be taken into account.