Interface Hamiltonians and bulk critical behavior.

We examine the derivation and use of a "d"-1 dimensional interface Hamiltonian to describe properties of a "d" dimensional liquid- vapor or Ising system near the critical point. We argue that such a simplified description, which ignores bulk excitations ("bubbles" of the opposite phase) and multiple-valued interface configurations ("overhangs") is valid only on length scales larger than the bulk correlation length xi(B). We examine several modifications to the usual Ising model for which in certain limits a single-valued interfacial description becomes exact. Such models either exhibit no bulk critical properties at all, even if the surface tension sigma vanishes, or have critical properties in a different universality class from the usual Ising model (liquid-vapor) critical point.