The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For $\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for $\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in $Z^3$.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

Nitrogen sources, transport and processing in peri-urban floodplains

Peri-urban floodplains are an important interface between developed land and the aquatic environment and may act as a source or sink for contaminants moving from urban areas towards surface water courses. With increasing pressure from urban development the functioning of floodplains is coming under greater scrutiny. A number of peri-urban sites have been found to be populated with legacy landfills which could potentially cause pollution of adjacent river bodies. Here, a peri-urban floodplain adjoining the city of Oxford, UK, with the River Thames has been investigated over a period of three years through repeated sampling of groundwaters from existing and specially constructed piezometers. A nearby landfill has been found to have imprinted a strong signal on the groundwater with particularly high concentrations of ammonium and generally low concentrations of nitrate and dissolved oxygen. An intensive study of nitrogen dynamics through the use of N-species chemistry, nitrogen isotopes and dissolved nitrous oxide reveals that there is little or no denitrification in the majority of the main landfill plume, and neither is the ammonium significantly retarded by sorption to the aquifer sediments. A simple model has determined the flux of total nitrogen and ammonium from the landfill, through the floodplain and into the river. Over an 8 km reach of the river, which has a number of other legacy landfills, it is estimated that 27.5 tonnes of ammonium may be delivered to the river annually. Although this is a relatively small contribution to the total river nitrogen, it may represent up to 15% of the ammonium loading at the study site and over the length of the reach could increase in-stream concentrations by nearly 40%. Catchment management plans that encompass floodplains in the peri-urban environment need to take into account the likely risk to groundwater and surface water quality that these environments pose

Competing interactions in the XYZ model

We study the interplay between a XY anisotropy $\gamma$, exchange modulations and an external magnetic field along the z direction in the XYZ chain using bosonization and Lanczos diagonalization techniques. We find an Ising critical line in the space of couplings which occur due to competing relevant perturbations which are present. More general situations are also discussed.Comment: 6 pages, 6 figure

ISML: an interface specification meta-language

In this paper we present an abstract metaphor model situated within a model-based user interface framework. The inclusion of metaphors in graphical user interfaces is a well established, but mostly craft-based strategy to design. A substantial body of notations and tools can be found within the model-based user interface design literature, however an explicit treatment of metaphor and its mappings to other design views has yet to be addressed. We introduce the Interface Specification Meta-Language (ISML) framework and demonstrate its use in comparing the semantic and syntactic features of an interactive system. Challenges facing this research are outlined and further work proposed

Differentiating normal and problem gambling: a grounded theory approach.

A previous study (Ricketts &amp; Macaskill, 2003) delineated a theory of problem gambling based on the experiences of treatment seeking male gamblers and allowed predictions to be made regarding the processes that differentiate between normal and problem gamblers. These predictions are the focus of the present study, which also utilised a grounded theory approach, but with a sample of male high frequency normal gamblers. The findings suggest that there are common aspects of gambling associated with arousal and a sense of achievement. The use of gambling to manage negative emotional states differentiated normal and problem gambling. Perceived self-efficacy , emotion management skills and perceived likelihood of winning money back were intervening variables differentiating problem and normal gamblers.</p

Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet

The exact expression derived by Bougourzi, Couture, and Kacir for the 2-spinon contribution to the dynamic spin structure factor $S_{zz}(q,\omega)$ of he one-dimensional $S$=1/2 Heisenberg antiferromagnet at $T=0$ is evaluated for direct comparison with finite-chain transition rates ($N\leq 28$) and an approximate analytical result previously inferred from finite-$N$ data, sum rules, and Bethe-ansatz calculations. The 2-spinon excitations account for 72.89% of the total intensity in $S_{zz}(q,\omega)$. The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the 2-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and $q$-dependent susceptibility are determined via sum rules.Comment: 6 pages (RevTex) and 5 figures (Postscript

High-field magnetization study of the S = 1/2 antiferromagnetic Heisenberg chain [PM Cu(NO3_3)2_2(H2_2O)2_2]n_n with a field-induced gap

We present a high-field magnetization study of the $S$ = 1/2 antiferromagnetic Heisenberg chain [PM Cu(NO$_3$)$_2$(H$_2$O)$_2$]$_n$. For this material, as result of the Dzyaloshinskii-Moriya interaction and a staggered $g$ tensor, the ground state is characterized by an anisotropic field-induced spin excitation gap and a staggered magnetization. Our data reveal the qualitatively different behavior in the directions of maximum and zero spin excitation gap. The data are analyzed via exact diagonalization of a linear spin chain with up to 20 sites and on basis of the Bethe ansatz equations, respectively. For both directions we find very good agreement between experimental data and theoretical calculations. We extract the magnetic coupling strength $J/k_B$ along the chain direction to 36.3(5) K and determine the field dependence of the staggered magnetization component $m_s$.Comment: 5 pages, 2 figures (minor changes to manuscript and figures

Antiferromagnetic Zigzag Spin Chain in Magnetic Fields at Finite Temperatures

We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process($M$-$H$ curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization, susceptibility and specific heat of the zigzag chain in magnetic fields at finite temperatures, and then discuss how the calculated quantities reflect the low-lying excitations of the system related with the critical behaviors in the $M$-$H$ curve.Comment: accepted for publication in Physical Review

One-dimensional spin-1/2 Heisenberg antiferromagnet in a weak external magnetic field

The one dimensional spin-1/2 Heisenberg antiferromagnet in a weak magnetic field h is studied using the bosonization method. We derive a set of renormalization group equations. The fixed point is reached when the field is scaled to the value at which the system is quarter-filled. As the magnetic field varies, a continuum line of fixed points is formed. We compute the uniform longitudinal susceptibility $\chi_z(h)$. The singular behavior of $\chi_z(h)$ as $h\to 0$ is found to be contained in $1/\ln(h_o/h)$ with $h_o$ a non-universal constant. The spin-spin correlations in the magnetic field are calculated.Comment: 5 pages, 1 figure, published on PR