Projection Estimates of Constrained Functional Parameters

AMS classifications: 62G05; 62G07; 62G08; 62G20; 62G32;estimation;convex function;extreme value copula;Pickands dependence function;projection;shape constraint;support function;tangent cone

Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory

For an anisotropic euclidean $\phi^4$-theory with two interactions [u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for $M \geq 3$ is found, implying that the critical exponents in the magnetic phase transition of real crystals are of the cubic universality class. There were previous indications of the stability based either on lower-loop expansions or on less reliable Pad\'{e approximations, but only the evidence presented in this work seems to be sufficently convincing to draw this conclusion.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.htm

Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length

We extend previous work on applying the epsilon-expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in epsilon=4-d, where d is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure

New geometries for high spatial resolution hall probes

The Hall response function of symmetric and asymmetric planar Hall effect devices is investigated by scanning a magnetized tip above a sensor surface while simultaneously recording the topography and the Hall voltage. Hall sensor geometries are tailored using a Focused Ion Beam, in standard symmetric and new asymmetric geometries. With this technique we are able to reduce a single voltage probe to a narrow constriction 20 times smaller than the other device dimensions. We show that the response function is peaked above the constriction, in agreement with numerical simulations. The results suggest a new way to pattern Hall sensors for enhanced spatial resolution.Comment: 12 pages, 5 figures, submitted to Journal of Applied Physic

New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop \epsilon expansions

A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the exact asymptotic parameters to be known. The method is tested on functions expanded in their asymptotic power series. It is applied to estimating the critical exponent values for an N-vector field model, describing magnetic and structural phase transitions in cubic and tetragonal crystals, from five-loop \epsilon expansions.Comment: 9 pages, LaTeX, 3 PostScript figure