Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $\alpha$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.Comment: 25 pages, 4 figures, 8 table

Interactions suppress Quasiparticle Tunneling at Hall Bar Constrictions

Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly-pinched quantum-point-contact constrictions, in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.Comment: 4 page

TMD PDF's: gauge invariance, RG properties and Wilson lines

The UV divergences associated with transverse-momentum dependent (TMD) parton distribution functions (PDF) are calculated together with the ensuing one-loop anomalous dimensions in the light-cone gauge. Time-reversal-odd effects in the anomalous dimensions are observed and the role of Glauber gluons is discussed. A generalized renormalization procedure of TMD PDFs is proposed, relying upon the renormalization of contour-dependent operators with obstructions.Comment: 4 pages, 1 figure. Talk presented at the International Workshop on Diffraction in High Energy and Nuclear Physics, La Londe-les-Maures, France, 9-14 Sept 2008. v2: 5 pages, preprint number and e-mail addresses adde

Perforated Duodenal Ulcer in Pregnancy—A Rare Cause of Acute Abdominal Pain in Pregnancy: A Case Report and Literature Review

Medical and surgical disorders in pregnancy can be can be quite challenging for the obstetrician gynaecologist even in resource rich countries. Reaching an accurate diagnosis and admininstering appropriate management can be difficult in the presence of an on-going pregnancy. The importance of involving specialist from other disciplines (multidisciplinary care) cannot be overemphasized. We present an interesting case of perforated duodenal ulcer in a pregnant patient, review the literature ,discuss the differential diagnosis and evaluate the management principles for this rare condition

Exclusive quasielastic production of dijets at hadronic colliders

We critically re-examine the calculation of central production of dijets in quasi-elastic hadronic collisions. We find that the process is not dominated by the perturbative contribution, and discuss several sources of uncertainties in the calculation.Comment: 4 pages, talk given at Diffraction-2008, La Londe-les-Maures, France, 9-14 Sept 200

gamma* -> rhoT impact factor with twist three accuracy

We evaluate the impact factor of the transition gamma* -> rhoT taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. Our results are free of end-point singularities. This opens the way to a consistent treatment of factorization for exclusive processes with a transversally polarized vector meson.Comment: 4 pages, 1 figure; To appear in the proceedings of Diffraction 2008: International Workshop on Diffraction in High-Energy Physics, La Londe-les-Maures, France, September 9-14, 200

Tails of probability density for sums of random independent variables

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for $p_{_N}(x)$ differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for $p_{_N}(x)$. However, the tail is not Gaussian even if the variances are finite. In the latter case $p_{_N}(x)$ has two different asymptotics. At small and moderate values of $x$ the distribution is Gaussian. At large $x$ the non-Gaussian tail arises. The crossover between the two asymptotics occurs at $x$ proportional to $N$. For this reason the non-Gaussian tail exists at finite $N$ only. In the limit $N$ tends to infinity the origin of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the distribution of the random terms the non-Gaussian tail may decay either slower than the Gaussian, or faster than it. A number of particular examples is discussed in detail.Comment: 6 pages, 4 figure

Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models

In this paper we study the critical exponents of the quantum sine-Gordon and U(1) Thirring models in the incommensurate phase. This phase appears when the chemical potential $h$ exceeds a critical value and is characterized by a finite density of solitons. The low-energy sector of this phase is critical and is described by the Gaussian model (Tomonaga-Luttinger liquid) with the compactification radius dependent on the soliton density and the sine-Gordon model coupling constant $\beta$. For a fixed value of $\beta$, we find that the Luttinger parameter $K$ is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value $\beta^2/8\pi$ away from it. We describe a possible phase diagram of the model consisting of an array of weakly coupled chains. The possible phases are Fermi liquid, Spin Density Wave, Spin-Peierls and Wigner crystal.Comment: 10pages; Improved version; Submitted to Physical Review

Edge State Tunneling in a Split Hall Bar Model

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.Comment: 13 pages, including 4 figures,final version as publishe