13 research outputs found
Functional Renormalization Description of the Roughening Transition
We reconsider the problem of the static thermal roughening of an elastic
manifold at the critical dimension in a periodic potential, using a
perturbative Functional Renormalization Group approach. Our aim is to describe
the effective potential seen by the manifold below the roughening temperature
on large length scales. We obtain analytically a flow equation for the
potential and surface tension of the manifold, valid at all temperatures. On a
length scale , the renormalized potential is made up of a succession of
quasi parabolic wells, matching onto one another in a singular region of width
for large . We also obtain numerically the step energy as a
function of temperature, and relate our results to the existing experimental
data on He. Finally, we sketch the scenario expected for an arbitrary
dimension and examine the case of a non local elasticity which is
realized physically for the contact line.Comment: 21 pages, 2 .ps figures. Submitted to E.P.J.
Comment on ``Roughening Transition of Interfaces in Disordered Media''
Emig and Nattermann (Phys. Rev. Lett. 81, 1469 (1998)) have recently
investigated the competition between lattice pinning and impurity pinning using
a Renormalisation Group (RG) approach. For elastic objects of internal
dimensions , they find, at zero temperature, an interesting second
order phase transition between a flat phase for small disorder and a rough
phase for large disorder. These results contrast with those obtained using the
replica variational approach for the same problem, where a first order
transition between flat and rough phases was predicted. In this comment, we
show that these results can be reconciled by analysing the RG flow for an
arbitrary dimension for the displacement field.Comment: Submitted to Phys. Rev. Let
Domain wall roughening in dipolar films in the presence of disorder
We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domain
wall in a thin film with in-plane magnetization, where we consider the
contribution of the long-range dipolar interaction beyond the quadratic
approximation. We show that such a Hamiltonian is analogous to the Hamiltonian
of a one-dimensional polaron in an external random potential. We use a replica
variational method to compute the roughening exponent of the domain wall for
the case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and
references 1,2 and 12 were added to conform with the referee's repor
Wandering of a contact line at thermal equilibrium
We reconsider the problem of the solid-liquid-vapour contact-line on a
disordered substrate, in the collective pinning regime. We go beyond scaling
arguments and perform an analytic computation, through the replica variational
method, of the fluctuations of the line. We show how gravity effects must be
included for a proper quantitative comparison with available experimental data
of the wetting of liquid helium on a caesium substrate. The theoretical result
is in good agreement with experimental findings for this case.Comment: 24 laTex pages with 5 EPS figures included. submitted to Phys. Rev
Dissipation in Dynamics of a Moving Contact Line
The dynamics of the deformations of a moving contact line is studied assuming
two different dissipation mechanisms. It is shown that the characteristic
relaxation time for a deformation of wavelength of a contact line
moving with velocity is given as . The velocity
dependence of is shown to drastically depend on the dissipation
mechanism: we find for the case when the dynamics is governed
by microscopic jumps of single molecules at the tip (Blake mechanism), and
when viscous hydrodynamic losses inside the moving
liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated
dominant dissipation mechanism can be experimentally determined using
relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T.
Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].Comment: REVTEX 8 pages, 9 PS figure
Width distribution of contact lines on a disordered substrate
We have studied the roughness of a contact line of a liquid meniscus on a
disordered substrate by measuring its width distribution. The comparison
between the measured width distribution and the width distribution calculated
in previous works, extended here to the case of open boundary conditions,
confirms that the Joanny-de Gennes model is not sufficient to describe the
dynamics of contact lines at the depinning threshold. This conclusion is in
agreement with recent measurements which determine the roughness exponent by
extrapolation to large system sizes.Comment: 4 pages, 3 figure
Roughening Transition in a Moving Contact Line
The dynamics of the deformations of a moving contact line on a disordered
substrate is formulated, taking into account both local and hydrodynamic
dissipation mechanisms. It is shown that both the coating transition in contact
lines receding at relatively high velocities, and the pinning transition for
slowly moving contact lines, can be understood in a unified framework as
roughening transitions in the contact line. We propose a phase diagram for the
system in which the phase boundaries corresponding to the coating transition
and the pinning transition meet at a junction point, and suggest that for
sufficiently strong disorder a receding contact line will leave a
Landau--Levich film immediately after depinning. This effect may be relevant to
a recent experimental observation in a liquid Helium contact line on a Cesium
substrate [C. Guthmann, R. Gombrowicz, V. Repain, and E. Rolley, Phys. Rev.
Lett. {\bf 80}, 2865 (1998)].Comment: 16 pages, 6 encapsulated figure
Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions
The large distance behaviors of the random field and random anisotropy O(N)
models are studied with the functional renormalization group in 4-\epsilon
dimensions. The random anisotropy Heisenberg (N=3) model is found to have a
phase with the infinite correlation radius at low temperatures and weak
disorder. The correlation function of the magnetization obeys a power law <
m(x) m(y) >\sim |x-y|^{-0.62\epsilon}. The magnetic susceptibility diverges at
low fields as \chi \sim H^{-1+0.15\epsilon}. In the random field O(N) model the
correlation radius is found to be finite at the arbitrarily weak disorder for
any N>3. The random field case is studied with a new simple method, based on a
rigorous inequality. This approach allows one to avoid the integration of the
functional renormalization group equations.Comment: 12 pages, RevTeX; a minor change in the list of reference
Exact Renormalization Group Equations. An Introductory Review
We critically review the use of the exact renormalization group equations
(ERGE) in the framework of the scalar theory. We lay emphasis on the existence
of different versions of the ERGE and on an approximation method to solve it:
the derivative expansion. The leading order of this expansion appears as an
excellent textbook example to underline the nonperturbative features of the
Wilson renormalization group theory. We limit ourselves to the consideration of
the scalar field (this is why it is an introductory review) but the reader will
find (at the end of the review) a set of references to existing studies on more
complex systems.Comment: Final version to appear in Phys. Rep.; Many references added, section
4.2 added, minor corrections. 65 pages, 6 fig