Percolation properties of the 2D Heisenberg model

We analyze the percolation properties of certain clusters defined on configurations of the 2--dimensional Heisenberg model. We find that, given any direction \vec{n} in O(3) space, the spins almost perpendicular to \vec{n} form a percolating cluster. This result gives indications of how the model can avoid a previously conjectured Kosterlitz-Thouless phase transition at finite temperature T.Comment: 4 pages, 3 eps figures. Revised version (more clear abstract, some new references

Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass

The two dimensional XY spin glass is studied numerically by a finite size scaling method at T=0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T. Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent $\nu \approx 2.70$. We obtain preliminary results in 3d.Comment: 4 pages, 2 figures, revte

Numerical Study of Order in a Gauge Glass Model

The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state configuration for a given realization of disorder. A numerical technique, which is exact in principle, is used to evaluate this energy and to estimate the stiffness exponent $\theta$. This method gives $\theta = -0.36\pm0.013$ in 2d and $\theta = +0.31\pm 0.015$ in 3d, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let

Monte Carlo simulation of a two-dimensional continuum Coulomb gas

We study the classical two-dimensional Coulomb gas model for thermal vortex fluctuations in thin superconducting/superfluid films by Monte Carlo simulation of a grand canonical vortex ensemble defined on a continuum. The Kosterlitz-Thouless transition is well understood at low vortex density, but at high vortex density the nature of the phase diagram and of the vortex phase transition is less clear. From our Monte Carlo data we construct phase diagrams for the 2D Coulomb gas without any restrictions on the vortex density. For negative vortex chemical potential (positive vortex core energy) we always find a Kosterlitz-Thouless transition. Only if the Coulomb interaction is supplemented with a short-distance repulsion, a first order transition line is found, above some positive value of the vortex chemical potential.Comment: 10 pages RevTeX, 7 postscript figures included using eps

Positional Disorder (Random Gaussian Phase Shifts) in the Fully Frustrated Josephson Junction Array (2D XY Model)

We consider the effect of positional disorder on a Josephson junction array with an applied magnetic field of f=1/2 flux quantum per unit cell. This is equivalent to the problem of random Gaussian phase shifts in the fully frustrated 2D XY model. Using simple analytical arguments and numerical simulations, we present evidence that the ground state vortex lattice of the pure model becomes disordered, in the thermodynamic limit, by any amount of positional disorder.Comment: 4 pages, 4 eps figures embedde

Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts

The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\pm J$ XY spin glass in 3D, we obtain a spin stiffness exponent $\theta_{s} \approx +0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain $\theta_{s}< 0$. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale $L$. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.Comment: 14 pages, 9 figures, revtex

Vortex Lattice Melting in 2D Superconducting Networks and Films

We carry out MC studies of 2D superconducting networks, in an applied magnetic field, for square and honeycomb geometries. We consider both dilute systems (f=1/q) and systems near full frustration (f=1/2-1/q). For the dilute case (which models a film as q->infinity), we find two transitions: at T_c(f)~1/q there is a depinning transition from a pinned to a floating vortex lattice; at T_m(f)~constant the floating vortex lattice melts into an isotropic liquid. We analyze this melting according to the Kosterlitz- Thouless theory of dislocation mediated melting, and find that the melting is weakly first order. For the case near full frustration, the system can be described in terms of the density of defects in an otherwise fully frustrated vortex pattern. We find pinned solid, floating solid, and liquid defect phases, as well as a higher sharp transition corresponding to the disordering of the fully frustrated background.Comment: 55 pages, RevTex3.0, 25 figures (available by mail by contacting [email protected]

Nodes of Ranvier and Paranodes in Chronic Acquired Neuropathies

Chronic acquired neuropathies of unknown origin are classified as chronic inflammatory demyelinating polyneuropathies (CIDP) and chronic idiopathic axonal polyneuropathies (CIAP). The diagnosis can be very difficult, although it has important therapeutic implications since CIDP can be improved by immunomodulating treatment. The aim of this study was to examine the possible abnormalities of nodal and paranodal regions in these two types of neuropathies. Longitudinal sections of superficial peroneal nerves were obtained from biopsy material from 12 patients with CIDP and 10 patients with CIAP and studied by immunofluorescence and in some cases electron microscopy. Electron microscopy revealed multiple alterations in the nodal and paranodal regions which predominated in Schwann cells in CIDP and in axons in CIAP. In CIDP paranodin/Caspr immunofluorescence was more widespread than in control nerves, extending along the axon in internodes where it appeared intense. Nodal channels Nav and KCNQ2 were less altered but were also detected in the internodes. In CIAP paranodes, paranodin labeling was irregular and/or decreased. To test the consequences of acquired primary Schwann cells alteration on axonal proteins, we used a mouse model based on induced deletion of the transcription factor Krox-20 gene. In the demyelinated sciatic nerves of these mice we observed alterations similar to those found in CIDP by immunofluorescence, and immunoblotting demonstrated increased levels of paranodin. Finally we examined whether the alterations in paranodin immunoreactivity could have a diagnosis value. In a sample of 16 biopsies, the study of paranodin immunofluorescence by blind evaluators led to correct diagnosis in 70±4% of the cases. This study characterizes for the first time the abnormalities of nodes of Ranvier in CIAP and CIDP, and the altered expression and distribution of nodal and paranodal proteins. Marked differences were observed between CIDP and CIAP and the alterations in paranodin immunofluorescence may be an interesting tool for their differential diagnosis