21,638 research outputs found

### An Evening Spent with Bill van Zwet

Willem Rutger van Zwet was born in Leiden, the Netherlands, on March 31,
1934. He received his high school education at the Gymnasium Haganum in The
Hague and obtained his Masters degree in Mathematics at the University of
Leiden in 1959. After serving in the army for almost two years, he obtained his
Ph.D. at the University of Amsterdam in 1964, with Jan Hemelrijk as advisor. In
1965, he was appointed Associate Professor of Statistics at the University of
Leiden and promoted to Full Professor in 1968. He remained in Leiden until his
retirement in 1999, while also serving as Associate Professor at the University
of Oregon (1965), William Newman Professor at the University of North Carolina
at Chapel Hill (1990--1996), frequent visitor and Miller Professor (1997) at
the University of California at Berkeley, director of the Thomas Stieltjes
Institute of Mathematics in the Netherlands (1992--1999), and founding director
of the European research institute EURANDOM (1997--2000). At Leiden, he was
Dean of the School of Mathematics and Natural Sciences (1982--1984). He served
as chair of the scientific council and member of the board of the Mathematics
Centre at Amsterdam (1983--1996) and the Leiden University Fund (1993--2005).Comment: Published in at http://dx.doi.org/10.1214/08-STS261 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org

### STM Studies of TbTe3: Evidence for a fully Incommensurate Charge Density Wave

We observe unidirectional charge density wave ordering on the cleaved surface
of TbTe3 with a Scanning Tunneling Microscope at ~6 K. The modulation
wave-vector q_{CDW} as determined by Fourier analysis is 0.71 +/- 0.02 * 2
pi/c. (Where c is one edge of the in-plane 3D unit cell.) Images at different
tip-sample voltages show the unit cell doubling effects of dimerization and the
layer below. Our results agree with bulk X-ray measurements, with the addition
of ~(1/3) * 2 pi/a ordering perpendicular to the CDW. Our analysis indicates
that the CDW is incommensurate.Comment: 4 pages, 4 figure

### QCD traveling waves beyond leading logarithms

We derive the asymptotic traveling-wave solutions of the nonlinear
1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in
momentum-space, with 1-loop running coupling constant and equipped with the
Balitsky-Kovchegov-Kuraev-Lipatov kernel at next-to-leading logarithmic
accuracy, conveniently regularized by different resummation schemes. Traveling
waves allow to define "universality classes" of asymptotic solutions, i.e.
independent of initial conditions and of the nonlinear damping. A dependence on
the resummation scheme remains, which is analyzed in terms of geometric scaling
properties.Comment: 10 pages, 5 figures; typos corrected, references updated, final
Phys.Rev. D versio

### Gas-liquid critical point in ionic fluids

Based on the method of collective variables we develop the statistical field
theory for the study of a simple charge-asymmetric $1:z$ primitive model (SPM).
It is shown that the well-known approximations for the free energy, in
particular DHLL and ORPA, can be obtained within the framework of this theory.
In order to study the gas-liquid critical point of SPM we propose the method
for the calculation of chemical potential conjugate to the total number density
which allows us to take into account the higher order fluctuation effects. As a
result, the gas-liquid phase diagrams are calculated for $z=2-4$. The results
demonstrate the qualitative agreement with MC simulation data: critical
temperature decreases when $z$ increases and critical density increases rapidly
with $z$.Comment: 18 pages, 1 figur

### Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model

We study the spin-1/2 Heisenberg model on the square lattice with first- and
second-neighbor antiferromagnetic interactions J1 and J2, which possesses a
nonmagnetic region that has been debated for many years and might realize the
interesting Z2 spin liquid. We use the density matrix renormalization group
approach with explicit implementation of SU(2) spin rotation symmetry and study
the model accurately on open cylinders with different boundary conditions. With
increasing J2, we find a Neel phase, a plaquette valence-bond (PVB) phase with
a finite spin gap, and a possible spin liquid in a small region of J2 between
these two phases. From the finite-size scaling of the magnetic order parameter,
we estimate that the Neel order vanishes at J2/J1~0.44. For 0.5<J2/J1<0.61, we
find dimer correlations and PVB textures whose decay lengths grow strongly with
increasing system width, consistent with a long-range PVB order in the
two-dimensional limit. The dimer-dimer correlations reveal the s-wave character
of the PVB order. For 0.44<J2/J1<0.5, spin order, dimer order, and spin gap are
small on finite-size systems and appear to scale to zero with increasing system
width, which is consistent with a possible gapless SL or a near-critical
behavior. We compare and contrast our results with earlier numerical studies.Comment: 11 pages, 17 figures, and 1 tabl

### Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found
evidence for a 2D spin liquid in proximity to the metal-insulator transition. A
Gutzwiller wavefunction study of the triangular lattice Heisenberg model with
appropriate four-spin ring exchanges has found that the projected spinon Fermi
sea state has a low variational energy. This wavefunction, together with a
slave particle gauge theory, suggests that such spin liquid possesses spin
correlations that are singular along surfaces in momentum space ("Bose
surfaces"). Signatures of this state, which we refer to as a "Spin Bose-Metal"
(SBM), are expected to be manifest in quasi-1D ladder systems: The discrete
transverse momenta cut through the 2D Bose surface leading to a distinct
pattern of 1D gapless modes. Here we search for a quasi-1D descendant of the
triangular lattice SBM state by exploring the Heisenberg plus ring model on a
two-leg strip (zigzag chain). Using DMRG, variational wavefunctions, and a
Bosonization analysis, we map out the full phase diagram. Without ring exchange
the model is equivalent to the J_1 - J_2 Heisenberg chain, and we find the
expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange
reveals a new gapless phase over a large swath of the phase diagram. Spin and
dimer correlations possess particular singular wavevectors and allow us to
identify this phase as the hoped for quasi-1D descendant SBM state. We derive a
low energy theory and find three gapless modes and one Luttinger parameter
controlling all power laws. Potential instabilities out of the zigzag SBM give
rise to other interesting phases such as a period-3 VBS or a period-4 Chirality
order, which we discover in the DMRG; we also find an interesting SBM state
with partial ferromagnetism.Comment: 30 pages, 23 figure

### Geometric scaling as traveling waves

We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-
Piscounov (KPP) equation to the problem of high energy evolution of the QCD
amplitudes. We explain how the traveling wave solutions of this equation are
related to geometric scaling, a phenomenon observed in deep-inelastic
scattering experiments. Geometric scaling is for the first time shown to result
from an exact solution of nonlinear QCD evolution equations. Using general
results on the KPP equation, we compute the velocity of the wave front, which
gives the full high energy dependence of the saturation scale.Comment: 4 pages, 1 figure. v2: references adde

### Universality and tree structure of high energy QCD

Using non-trivial mathematical properties of a class of nonlinear evolution
equations, we obtain the universal terms in the asymptotic expansion in
rapidity of the saturation scale and of the unintegrated gluon density from the
Balitsky-Kovchegov equation. These terms are independent of the initial
conditions and of the details of the equation. The last subasymptotic terms are
new results and complete the list of all possible universal contributions.
Universality is interpreted in a general qualitative picture of high energy
scattering, in which a scattering process corresponds to a tree structure
probed by a given source.Comment: 4 pages, 3 figure

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