Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry

In the framework of mean-field theory the equation for the order-parameter profile in a spherically-symmetric geometry at the bulk critical point reduces to an Emden-Fowler problem. We obtain analytic solutions for the surface universality class of extraordinary transitions in $d=4$ for a spherical shell, which may serve as a starting point for a pertubative calculation. It is demonstrated that the solution correctly reproduces the Fisher-de Gennes effect in the limit of the parallel-plate geometry.Comment: (to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded postscript file, 8-9

New Criticality of 1D Fermions

One-dimensional massive quantum particles (or 1+1-dimensional random walks) with short-ranged multi-particle interactions are studied by exact renormalization group methods. With repulsive pair forces, such particles are known to scale as free fermions. With finite $m$-body forces (m = 3,4,...), a critical instability is found, indicating the transition to a fermionic bound state. These unbinding transitions represent new universality classes of interacting fermions relevant to polymer and membrane systems. Implications for massless fermions, e.g. in the Hubbard model, are also noted. (to appear in Phys. Rev. Lett.)Comment: 10 pages (latex), with 2 figures (not included

Cumulant ratios and their scaling functions for Ising systems in strip geometries

We calculate the fourth-order cumulant ratio (proposed by Binder) for the two-dimensional Ising model in a strip geometry L x oo. The Density Matrix Renormalization Group method enables us to consider typical open boundary conditions up to L=200. Universal scaling functions of the cumulant ratio are determined for strips with parallel as well as opposing surface fields.Comment: 4 pages, RevTex, one .eps figure; references added, format change

Casimir Dispersion Forces and Orientational Pairwise Additivity

A path integral formulation is used to study the fluctuation-induced interactions between manifolds of arbitrary shape at large separations. It is shown that the form of the interactions crucially depends on the choice of the boundary condition. In particular, whether or not the Casimir interaction is pairwise additive is shown to depend on whether the ``metallic'' boundary condition corresponds to a ``grounded'' or an ``isolated'' manifold.Comment: 6 pages, RevTe

The NuTeV Anomaly, Neutrino Mixing, and a Heavy Higgs Boson

Recent results from the NuTeV experiment at Fermilab and the deviation of the Z invisible width, measured at LEP/SLC, from its Standard Model (SM) prediction suggest the suppression of neutrino-Z couplings. Such suppressions occur naturally in models which mix the neutrinos with heavy gauge singlet states. We postulate a universal suppression of the Z-nu-nu couplings by a factor of (1-epsilon) and perform a fit to the Z-pole and NuTeV observables with epsilon and the oblique correction parameters S and T. Compared to a fit with S and T only, inclusion of epsilon leads to a dramatic improvement in the quality of the fit. The values of S and T preferred by the fit can be obtained within the SM by a simple increase in the Higgs boson mass. However, if the W mass is also included in the fit, a non-zero U parameter becomes necessary which cannot be supplied within the SM. The preferred value of epsilon suggests that the seesaw mechanism may not be the reason why neutrinos are so light.Comment: 19 pages, REVTeX4, 8 postscript figures. Updated references. Typos correcte

Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes

The critical behavior of semi-infinite $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ and short-range interactions is investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated $m$ modulation axes are presumed to be parallel to the surface, where $0\le m\le d-1$. An appropriate semi-infinite $|\bm{\phi}|^4$ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term $\propto \bm{\phi}^2$ of the Hamiltonian must be supplemented by one of the form $\mathring{\lambda} \sum_{\alpha=1}^m(\partial\bm{\phi}/\partial x_\alpha)^2$ involving a dimensionless (renormalized) coupling constant $\lambda$. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension $d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value $\lambda^*$ if $\epsilon\equiv d^*(m)-d>0$. The surface critical exponents of the ordinary transition are determined to second order in $\epsilon$. Extrapolations of these $\epsilon$ expansions yield values of these exponents for $d=3$ in good agreement with recent Monte Carlo results for the case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by $d+m (\theta-1)$, where $\theta=\nu_{l4}/\nu_{l2}$ is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to generate some graphs; to appear in PRB; v2: some references and additional remarks added, labeling in figure 1 and some typos correcte

Apparent phase transitions in finite one-dimensional sine-Gordon lattices

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.Comment: 7 pages, 4 figure

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.Comment: 56 pages, RevTeX, 20 Figure

Standard Model Confronting New Results for epsilon'/epsilon

We analyze the CP violating ratio \epe=epsilon'/epsilon in the Standard Model in view of the new KTeV results. We review the present status of the most important non-perturbative parameters B_6, B_8, B_K and of the strange quark mass m_s. We also briefly discuss the issues of final state interactions and renormalization scheme dependence. Updating the values of the CKM parameters, of m_t and Lambda (MSbar) and using Gaussian errors for the experimental input and flat distributions for the theoretical parameters we find \epe substantially below the NA31 and KTeV data: \epe= (7.7^{+6.0}_{-3.5}) 10^{-4} and \epe= (5.2^{+4.6}_{-2.7}) 10^{-4} in the NDR and HV renormalization schemes respectively. A simple scanning of all input parameters gives on the other hand 1.05 10^{-4} < \epe < 28.8 10^{-4} and 0.26 10^{-4} < \epe < 22.0 10^{-4} respectively. Analyzing the dependence on various parameters we find that only for extreme values of B_6, B_8 and m_s and suitable values of CKM parameters and Lambda(MSbar), the ratio \epe can be made consistent with data. We analyze the impact of these data on the lower bounds for Im(V_{td}V_{ts}^*), Br(K_L to pi^0 nu barnu), Br(K_L to pi^0e^+e^-)_{dir} and on tan(beta) in the Two Higgs Doublet Model II.Comment: main latex-file, 4 figures and related latex files, 47 page

Exploring the Bimodal Solar System via Sample Return from the Main Asteroid Belt: The Case for Revisiting Ceres

Abstract: Sample return from a main-belt asteroid has not yet been attempted, but appears technologically feasible. While the cost implications are significant, the scientific case for such a mission appears overwhelming. As suggested by the “Grand Tack” model, the structure of the main belt was likely forged during the earliest stages of Solar System evolution in response to migration of the giant planets. Returning samples from the main belt has the potential to test such planet migration models and the related geochemical and isotopic concept of a bimodal Solar System. Isotopic studies demonstrate distinct compositional differences between samples believed to be derived from the outer Solar System (CC or carbonaceous chondrite group) and those that are thought to be derived from the inner Solar System (NC or non-carbonaceous group). These two groups are separated on relevant isotopic variation diagrams by a clear compositional gap. The interface between these two regions appears to be broadly coincident with the present location of the asteroid belt, which contains material derived from both groups. The Hayabusa mission to near-Earth asteroid (NEA) (25143) Itokawa has shown what can be learned from a sample-return mission to an asteroid, even with a very small amount of sample. One scenario for main-belt sample return involves a spacecraft launching a projectile that strikes an object and flying through the debris cloud, which would potentially allow multiple bodies to be sampled if a number of projectiles are used on different asteroids. Another scenario is the more traditional method of landing on an asteroid to obtain the sample. A significant range of main-belt asteroids are available as targets for a sample-return mission and such a mission would represent a first step in mineralogically and isotopically mapping the asteroid belt. We argue that a sample-return mission to the asteroid belt does not necessarily have to return material from both the NC and CC groups to viably test the bimodal Solar System paradigm, as material from the NC group is already abundantly available for study. Instead, there is overwhelming evidence that we have a very incomplete suite of CC-related samples. Based on our analysis, we advocate a dedicated sample-return mission to the dwarf planet (1) Ceres as the best means of further exploring inherent Solar System variation. Ceres is an ice-rich world that may be a displaced trans-Neptunian object. We almost certainly do not have any meteorites that closely resemble material that would be brought back from Ceres. The rich heritage of data acquired by the Dawn mission makes a sample-return mission from Ceres logistically feasible at a realistic cost. No other potential main-belt target is capable of providing as much insight into the early Solar System as Ceres. Such a mission should be given the highest priority by the international scientific community