303 research outputs found
Finite temperature Functional RG, droplets and decaying Burgers Turbulence
The functional RG (FRG) approach to pinning of -dimensional manifolds is
reexamined at any temperature . A simple relation between the coupling
function and a physical observable is shown in any . In its
beta function is displayed to a high order, ambiguities resolved; for random
field disorder (Sinai model) we obtain exactly the T=0 fixed point as
well as its thermal boundary layer (TBL) form (i.e. for ) at .
Connection between FRG in and decaying Burgers is discussed. An exact
solution to the functional RG hierarchy in the TBL is obtained for any and
related to droplet probabilities.Comment: 8 pages 1 figur
Disorder induced transitions in layered Coulomb gases and application to flux lattices in superconductors
A layered system of charges with logarithmic interaction parallel to the
layers and random dipoles in each layer is studied via a variational method and
an energy rationale. These methods reproduce the known phase diagram for a
single layer where charges unbind by increasing either temperature or disorder,
as well as a freezing first order transition within the ordered phase.
Increasing interlayer coupling leads to successive transitions in which charge
rods correlated in N>1 neighboring layers are unbounded by weaker disorder.
Increasing disorder leads to transitions between different N phases. The method
is applied to flux lattices in layered superconductors in the limit of
vanishing Josephson coupling. The unbinding charges are point defects in the
flux lattice, i.e. vacancies or interstitials. We show that short range
disorder generates random dipoles for these defects. We predict and accurately
locate a disorder-induced defect-unbinding transition with loss of
superconducting order, upon increase of disorder. While N=1 charges dominate
for most system parameters, we propose that in multi-layer superconductors
defect rods can be realized.Comment: 26 pages, 6 figure
SLE on doubly-connected domains and the winding of loop-erased random walks
Two-dimensional loop-erased random walks (LERWs) are random planar curves
whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with
parameter k = 2. In this note, some properties of an SLE_k trace on
doubly-connected domains are studied and a connection to passive scalar
diffusion in a Burgers flow is emphasised. In particular, the endpoint
probability distribution and winding probabilities for SLE_2 on a cylinder,
starting from one boundary component and stopped when hitting the other, are
found. A relation of the result to conditioned one-dimensional Brownian motion
is pointed out. Moreover, this result permits to study the statistics of the
winding number for SLE_2 with fixed endpoints. A solution for the endpoint
distribution of SLE_4 on the cylinder is obtained and a relation to reflected
Brownian motion pointed out.Comment: 22 pages, 4 figure
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