Direction dependent free energy singularity of the asymmetric six-vertex model

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields $(h,v)$. In the $(h,v)$ plane, the phase boundary is approached along straight lines $\delta v=k \delta h$, where $(\delta h,\delta v)$ measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski-Talapov transition $\delta f \sim const (\delta h)^{3/2}$ for any direction other than the tangential one. In the latter case $\delta f$ shows a discontinuity in the third derivative.Comment: 18 pages, Latex, 1 figure, minor corrections and two references change

CCD BVRI and 2MASS Photometry of the Poorly Studied Open Cluster NGC 6631

Here we have obtained the {\it BVRI CCD} photometry down to a limiting magnitude of $V \sim$ 20 for the southern poorly studied open cluster NGC 6631. It is observed from the {\it 1.88 m} Telescope of Kottamia Observatory in Egypt. About 3300 stars have been observed in an area of $\sim 10^{\prime} \times 10^{\prime}$ around the cluster center. The main photometric parameters have been estimated and compared with the results that determined for the cluster using {\it JHKs 2MASS} photometric database. The cluster's diameter is estimated to be 10 arcmin; the reddening E(B-V)= 0.68 $\pm$ 0.10 mag, E(J-H)= 0.21 $\pm$ 0.10 mag, the true modulus (m-M)$_{o}$= 12.16 $\pm$ 0.10 mag, which corresponds to a distance of 2700 $\pm$125 pc and age of 500 $\pm$ 50 Myr.Comment: 13 pages, 6 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

WSRT Faraday tomography of the Galactic ISM at \lambda \sim 0.86 m

We investigate the distribution and properties of Faraday rotating and synchrotron emitting regions in the Galactic ISM in the direction of the Galactic anti-centre. We apply Faraday tomography to a radio polarization dataset that we obtained with the WSRT. We developed a new method to calculate a linear fit to periodic data, which we use to determine rotation measures from our polarization angle data. From simulations of a Faraday screen + noise we could determine how compatible the data are with Faraday screens. An unexpectedly large fraction of 14% of the lines-of-sight in our dataset show an unresolved main component in the Faraday depth spectrum. For lines-of-sight with a single unresolved component we demonstrate that a Faraday screen in front of a synchrotron emitting region that contains a turbulent magnetic field component can explain the data.Comment: 5 pages, 5 figures. Accepted for publication as a Letter to the Editor in A&