't Hooft-Polyakov monopoles in lattice SU(N)+adjoint Higgs theory

We investigate twisted C-periodic boundary conditions in SU(N) gauge field theory with an adjoint Higgs field. We show that with a suitable twist for even N one can impose a non-zero magnetic charge relative to residual U(1) gauge groups in the broken phase, thereby creating a 't Hooft-Polyakov magnetic monopole. This makes it possible to use lattice Monte-Carlo simulations to study the properties of these monopoles in the quantum theory.Comment: 15 pages, 6 figure

Utility, subjective probability, their interaction, and variance preferences

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66507/2/10.1177_002200276200600106.pd

Ferromagnetism in the Infinite-U Hubbard Model

We have studied the stability of the ferromagnetic state in the infinite-U Hubbard model on a square lattice by approximate diagonalization of finite lattices using the density matrix renormalization group technique. By studying lattices with up to 5X20 sites, we have found the ferromagnetic state to be stable below the hole density of 22 percent. Beyond 22 percent of hole doping, the total spin of the ground state decreased gradually to zero with increasing hole density.Comment: 13 pages, RevteX 3.0, seven figures appended in uuencoded form, correcting problems with uuencoded figure

Cluster update and recognition

We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are are defined by gray-scale differences within the image. Motivated by biological systems, we introduce the concept of neural inhibition to the Potts model realization of the segmentation problem. Including the inhibition term in the Hamiltonian results in enhanced contrast and thereby significantly improves segmentation quality. As a second benefit we can - after equilibration - directly identify the image segments as the clusters formed by the clustering algorithm. To construct a new spin configuration the algorithm performs the standard steps of (1) forming clusters and of (2) updating the spins in a cluster simultaneously. As opposed to standard algorithms, however, we share the interaction energy between the two steps. Thus the update probabilities are not independent of the interaction energies. As a consequence, we observe an acceleration of the relaxation by a factor of 10 compared to the Swendson and Wang procedure.Comment: 4 pages, 2 figure

Variationnal study of ferromagnetism in the t1-t2 Hubbard chain

A one-dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping is studied variationally. This allows to exclude saturated ferromagnetism for $U < U_c$. The variational boundary $U_c (n)$ has a minimum at a ``critical density'' $n_c$ and diverges for $n \rightarrow 1$.Comment: 5 pages, LateX and 1 postscript figure. To appear in Physica

On the critical level-curvature distribution

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.Comment: 4 pages, 3 figure

Star copolymers in porous environments: scaling and its manifestations

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair correlation function g(x)\sim x^{-a}. Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double \epsilon=4-d, \delta=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.Comment: 13 pages, 3 figure

Evolution of leaf-form in land plants linked to atmospheric CO2 decline in the Late Palaeozoic era

The widespread appearance of megaphyll leaves, with their branched veins and planate form, did not occur until the close of the Devonian period at about 360 Myr ago. This happened about 40 Myr after simple leafless vascular plants first colonized the land in the Late Silurian/Early Devonian, but the reason for the slow emergence of this common feature of present-day plants is presently unresolved. Here we show, in a series of quantitative analyses using fossil leaf characters and biophysical principles, that the delay was causally linked with a 90% drop in atmospheric pCO2 during the Late Palaeozoic era. In contrast to simulations for a typical Early Devonian land plant, possessing few stomata on leafless stems, those for a planate leaf with the same stomatal characteristics indicate that it would have suffered lethal overheating, because of greater interception of solar energy and low transpiration. When planate leaves first appeared in the Late Devonian and subsequently diversified in the Carboniferous period, they possessed substantially higher stomatal densities. This observation is consistent with the effects of the pCO2 on stomatal development and suggests that the evolution of planate leaves could only have occurred after an increase in stomatal density, allowing higher transpiration rates that were sufficient to maintain cool and viable leaf temperatures

The Geometry of PSR B0031-07

PSR B0031-07 is well known to exhibit three different modes of drifting sub-pulses (mode A, B and C). It has recently been shown that in a multifrequency observation, consisting of 2700 pulses, all driftmodes were visible at low frequencies, while at 4.85 GHz only mode-A drift or non-drifting emission was detected. This suggests that modes A and B are emitted in sub-beams, rotating at a fixed distance from the magnetic axis, with the mode-B sub-beams being closer to the magnetic axis than the mode-A sub-beams. Diffuse emission between the sub-beams can account for the non-drifting emission. Using the results of an analysis of simultaneous multifrequency observations of PSR B0031-07, we set out to construct a geometrical model that includes emission from both sub-beams and diffuse emission and describes the regions of the radio emission of PSR B0031-07 at each emission frequency for driftmodes A and B. Based on the vertical spacing between driftbands, we have determined the driftmode of each sequence of drift. To restrict the model, we calculated average polarisation and intensity characteristics for each driftmode and at each frequency. The model reproduces the observed polarisation and intensity characteristics, suggesting that diffuse emission plays an important role in the emission properties of PSR B0031-07. The model further suggests that the emission heights of this pulsar range from a few kilometers to a little over 10 kilometers above the pulsar surface. We also find that the relationships between height and frequency of emission that follow from curvature radiation and from plasma-frequency emission could not be used to reproduce the observed frequency dependence of the width of the average intensity profiles.Comment: 15 pages, 9 figures, 8 tables, accepted for publication in A&

Numerical Evidence of Luttinger and Fermi Liquid Behaviour in the 2D Hubbard Model

The two dimensional Hubbard model with a single spin-up electron interacting with a finite density of spin-down electrons is studied using the quantum Monte Carlotechnique, a new conjugate gradient method for the evaluation of the Edwards wavefunction ansatz, and the standard second order perturbation theory. We performed simulations up to 242 sites at $U/t=4$ reaching the zero temperature properties with no ``fermion sign problem'' and found a surprisingly good accuracy of the Edwards wavefunction ansatz at low density or low doping. The conjugate gradient method was then applied to system up to 1922 sites and infinite $U$ for the Edwards state. Fermi liquid theory seems to remain stable in 2D for all cases studied with the exception of the half filling case where a ``Luttinger like behavior'' survives in the Hubbard model , yielding a vanishing quasiparticle weight in the thermodynamic limit.Comment: 10 pages + 4 pictures, RevTex, SISSA 121/93/CM/M