Heriot-Watt Mathematics Report Series
HWM00-13, 15 Jun 2000
The Effect of Roughness Differences on the Unbinding of Interfaces
C J Boulter and A L Stella
In recent years there has been considerable interest in the
effect of disorder on the nature and universality of wetting transitions.
One of the most frequently studied systems is that in which
geometrical disorder is present in the form of substrate roughness.
In 2D there is compelling evidence that the critical wetting transition found
for a flat substrate may become first order when surface roughness is
In particular if the roughness exponent of the wall exceeds the anisotropy
index of interface fluctuations in the bulk then first order wetting is found.
Here we extend the investigation of roughness induced effects to
the situation in which we have unbinding of two fluctuating interfaces
characterized by different roughness exponents $\zeta_1$ and $\zeta_2$ say
(e.g. a fluid membrane depinning from a liquid-vapour interface) in
the absence of quenched disorder.
In this case symmetry prevents a change in order of the unbinding transition
as the rougnesses are varied, however the critical behaviour is again found to
be controlled by the maximum of $\zeta_1$ and $\zeta_2$.
In addition our results depend quantitatively on a non-universal parameter
related to the relative curvature of the two interfaces whenever $\zeta_1
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