Structure of the axonal surface recognition molecule neurofascin and its relationship to a neural subgroup of the immunoglobulin superfamily

The chick axon-associated surface glycoprotein neurofascin is implicated in axonal growth and fasciculation as revealed by antibody perturbation experiments. Here we report the complete cDNA sequence of neurofascin. It is composed of four structural elements: At the NH2 terminus neurofascin contains six Ig-like motifs of the C2 subcategory followed by four fibronectin type III (FNIII)-related repeats. Between the FNIII-like repeats and the plasma membrane spanning region neurofascin contains a domain 75-amino acid residues-long rich in proline, alanine and threonine which might be the target of extensive O-linked glycosylation. A transmembrane segment is followed by a 113-amino acid residues-long cytoplasmic domain. Sequence comparisons indicate that neurofascin is most closely related to chick Nr-CAM and forms with L1 (Ng-CAM) and Nr-CAM a subgroup within the vertebrate Ig superfamily. Sequencing of several overlapping cDNA probes reveals interesting heterogeneities throughout the neurofascin polypeptide. Genomic Southern blots analyzed with neurofascin cDNA clones suggest that neurofascin is encoded by a single gene and its pre-mRNA might be therefore alternatively spliced. Northern blot analysis with domain specific probes showed that neurofascin mRNAs of about 8.5 kb are expressed throughout development in embryonic brain but not in liver. Isolation of neurofascin by immunoaffinity chromatography results in several molecular mass components. To analyze their origin the amino-terminal sequences of several neurofascin components were determined. The NH2-terminal sequences of the 185, 160, and 110-135 kD components are all the same as the NH2 termini predicted by the cDNA sequence, whereas the other neurofascin components start with a sequence found in a putative alternatively spliced segment between the Ig- and FNIII-like part indicating that they are derived by proteolytic cleavage. A combination of enzymatic and chemical deglycosylation procedures and the analysis of peanut lectin binding reveals O- and N-linked carbohydrates on neurofascin components which might generate additional heterogeneity

Testing fixed points in the 2D O(3) non-linear sigma model

Using high statistic numerical results we investigate the properties of the O(3) non-linear 2D sigma-model. Our main concern is the detection of an hypothetical Kosterlitz-Thouless-like (KT) phase transition which would contradict the asymptotic freedom scenario. Our results do not support such a KT-like phase transition.Comment: Latex, 7 pgs, 4 eps-figures. Added more analysis on the KT-transition. 4-loop beta function contains corrections from D.-S.Shin (hep-lat/9810025). In a note-added we comment on the consequences of these corrections on our previous reference [16

Universality Class of O(N)O(N) Models

We point out that existing numerical data on the correlation length and magnetic susceptibility suggest that the two dimensional $O(3)$ model with standard action has critical exponent $\eta=1/4$, which is inconsistent with asymptotic freedom. This value of $\eta$ is also different from the one of the Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$ model at $\theta=\pi$.Comment: 8 pages, with 3 figures included, postscript. An error concerning the errors has been correcte

O(N) and RP^{N-1} Models in Two Dimensions

I provide evidence that the 2D $RP^{N-1}$ model for $N \ge 3$ is equivalent to the $O(N)$-invariant non-linear $\sigma$-model in the continuum limit. To this end, I mainly study particular versions of the models, to be called constraint models. I prove that the constraint $RP^{N-1}$ and $O(N)$ models are equivalent for sufficiently weak coupling. Numerical results for their step-scaling function of the running coupling $\bar{g}^2= m(L) L$ are presented. The data confirm that the constraint $O(N)$ model is in the samei universality class as the $O(N)$ model with standard action. I show that the differences in the finite size scaling curves of $RP^{N-1}$i and $O(N)$ models observed by Caracciolo et al. can be explained as a boundary effect. It is concluded, in contrast to Caracciolo et al., that $RP^{N-1}$ and $O(N)$ models share a unique universality class.Comment: 14 pages (latex) + 1 figure (Postscript) ,uuencode

Lattice artefacts and the running of the coupling constant

We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in the two dimensional O(3) nonlinear $\sigma$ model. To investigate the continuum limit we refine the lattice spacing from the $1\over 16$ value used by LWW up to $1\over 160$. We find that the lattice artefacts are much larger than estimated by LWW and that most likely the coupling constant runs slower than predicted by perturbation theory. A precise determination of the running in the continuum limit would require a controlled ansatz of extrapolation, which, we argue, is not presently available.Comment: 4 pages, 4 figures. To address the criticism that we are studying a different quantitiy than Luscher, Weisz and Wolff originally did, we introduced a new equation (2), a new paragraph discussing this issue and a new figure comparing the results obtained with our prescription to that obtained with the original one of Luscher, Weisz and Wolf

Logarithmic Corrections in the 2D XY Model

Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square $L \times L$ lattices, the scaling behavior of the susceptibility $\chi$ and correlation length $\xi$ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections $(ln L)^{-2r}$ in the finite-size scaling region and $(ln \xi)^{-2r}$ in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to $512^2$ we obtain $r = -0.0270(10)$, in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to $\xi \approx 140$ in the high-temperature phase, however, we arrive at quite a different estimate of $r = 0.0560(17)$, which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation.Comment: 13 pages, LaTeX + 8 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

The role of point-like topological excitations at criticality: from vortices to global monopoles

We determine the detailed thermodynamic behavior of vortices in the O(2) scalar model in 2D and of global monopoles in the O(3) model in 3D. We construct new numerical techniques, based on cluster decomposition algorithms, to analyze the point defect configurations. We find that these criteria produce results for the Kosterlitz-Thouless temperature in agreement with a topological transition between a polarizable insulator and a conductor, at which free topological charges appear in the system. For global monopoles we find no pair unbinding transition. Instead a transition to a dense state where pairs are no longer distinguishable occurs at T<Tc, without leading to long range disorder. We produce both extensive numerical evidence of this behavior as well as a semi-analytic treatment of the partition function for defects. General expectations for N=D>3 are drawn, based on the observed behavior.Comment: 14 pages, REVTEX, 13 eps figure

Scaling law of Wolff cluster surface energy

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality.Comment: 12 pages, 3 figures. To appear in PR

On the Critical Temperature of Non-Periodic Ising Models on Hexagonal Lattices

The critical temperature of layered Ising models on triangular and honeycomb lattices are calculated in simple, explicit form for arbitrary distribution of the couplings.Comment: to appear in Z. Phys. B., 8 pages plain TEX, 1 figure available upon reques