Heriot-Watt Mathematics Report Series
HWM97-59, 20 Jan 1999
Renormalization group flow of the stiffness matrix-free energy relation
C J Boulter and A O Parry
Abstract
In order to satisfy exact sum-rule requirements for correlation
function structure at complete wetting a two-field Hamiltonian
$H_I^{(2)}[l_1,l_2]$, modelling the coupling of order-paramter
fluctuations near the wall and unbinding interface, has been introduced.
The model is characterized by a stiffness matrix,
$\mbox{\boldmath $\Sigma$}(l_1,l_2)$, whose bare (unrenormalized)
elements are related to the mean-field free energy. We extend previous
renormalization group studies to include the position dependence of
the matrix elements and derive an elegant operator relationship which
shows that the flow of the cross-coupling term $\Sigma_{12}(l_1,l_2)$
parallels that of the free energy. This establishes the validity of a
stiffness matrix-free energy relation in the presence of fluctuation
effects at the marginal dimension $d=3$ for systems with short-ranged
forces. We further show that an analogous relation exists for systems
with long-ranged molecular interactions.
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