Recently, a Nonlocal Model of short-range wetting was proposed that seems to overcome
problems with simpler interfacial models. In this thesis we explore this model in detail,
laying the foundations for its use. We show how it can be derived from a microscopic
Hamiltonian by a careful coarse-graining procedure, based on a previous recipe proposed
by Fisher and Jin. In the Nonlocal Model the substrate-interface interaction is described
by a binding potential functional with an elegant diagrammatic expansion:
W = a1 ∽ + b1+ ∽ + · · · .
∽ ∽
This model has the same asymptotic renormalisation group behaviour as the simpler
model but with a much smaller critical region, explaining the mystery of 3D critical
wetting. It also has the correct form to satisfy the covariance relation for wedge filling.
We then proceed to check the robustness of the structure of the Nonlocal Model using
perturbation theory to study the consequences of the use of a more general microscopic
Hamiltonian. The model is robust to such generalisations whose only relevant effect is
the change of the values of the coefficients of the Nonlocal Model. These same remarks
are valid for the inclusion of a surface field: the generalised model still has the same
structure, albeit with different coefficients. Another important extension is the inclusion
of a longer-range substrate-fluid interaction or a bulk field.
We finalise with a chapter exploring the structure of the correlation function at meanfield
level. This allows us to prove that the Nonlocal Model obeys a sum-rule for complete
wetting, and shed light on why the critical region is so small in the Nonlocal Model. The
study of correlations at a capillary slit can provide a direct test of the Nonlocal Model
