6 research outputs found
Orientational order on curved surfaces - the high temperature region
We study orientational order, subject to thermal fluctuations, on a fixed
curved surface. We derive, in particular, the average density of zeros of
Gaussian distributed vector fields on a closed Riemannian manifold. Results are
compared with the density of disclination charges obtained from a Coulomb gas
model. Our model describes the disordered state of two dimensional objects with
orientational degrees of freedom, such as vector ordering in Langmuir
monolayers and lipid bilayers above the hexatic to fluid transition.Comment: final version, 13 Pages, 2 figures, uses iopart.cl
B(H) Constitutive Relations Near H_c1 in Disordered Superconductors
We provide a self-contained account of the B vs. H constitutive relation near
H_c1 in Type II superconductors with various types of quenched random disorder.
The traditional Abrikosov result B ~ [ln (H - H_c1)]^{-2}, valid in the absence
of disorder and thermal fluctuations, changes significantly in the presence of
disorder. Moreover, the constitutive relations will depend strongly on the type
of disorder. In the presence of point disorder, B ~ (H - H_c1)^{3/2} in
three-dimensional (thick) superconductors, as shown by Nattermann and Lipowsky.
In two-dimensional (thin film) superconductors with point disorder, B ~ (H -
H_c1). In the presence of parallel columnar disorder, we find that B ~ exp[-C /
(H - H_c1)] in three dimensions, while B ~ exp[-K / (H - H_c1)^{1/2}] in two
dimensions. In the presence of nearly isotropically splayed disorder, we find
that B ~ (H - H_c1)^{3/2} in both two and three dimensions.Comment: 37 pages, 12 figures included in text; submitted to Physica
Vortex Pinning and the Non-Hermitian Mott Transition
The boson Hubbard model has been extensively studied as a model of the zero
temperature superfluid/insulator transition in Helium-4 on periodic substrates.
It can also serve as a model for vortex lines in superconductors with a
magnetic field parallel to a periodic array of columnar pins, due to a formal
analogy between the vortex lines and the statistical mechanics of quantum
bosons. When the magnetic field has a component perpendicular to the pins, this
analogy yields a non-Hermitian boson Hubbard model. At integer filling, we find
that for small transverse fields, the insulating phase is preserved, and the
transverse field is exponentially screened away from the boundaries of the
superconductor. At larger transverse fields, a ``superfluid'' phase of tilted,
entangled vortices appears. The universality class of the transition is found
to be that of vortex lines entering the Meissner phase at H_{c1}, with the
additional feature that the direction of the tilted vortices at the transition
bears a non-trivial relationship to the direction of the applied magnetic
field. The properties of the Mott Insulator and flux liquid phases with tilt
are also discussed.Comment: 20 pages, 12 figures included in text; to appear in Physical Review