7,712 research outputs found
Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models
Using detailed exact results on pair-correlation functions of Z-invariant
Ising models, we can write and run algorithms of polynomial complexity to
obtain wavevector-dependent susceptibilities for a variety of Ising systems.
Reviewing recent work we compare various periodic and quasiperiodic models,
where the couplings and/or the lattice may be aperiodic, and where the Ising
couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign.
We present some of our results on the square-lattice fully-frustrated Ising
model. Finally, we make a few remarks on our recent works on the pentagrid
Ising model and on overlapping unit cells in three dimensions and how these
works can be utilized once more detailed results for pair correlations in,
e.g., the eight-vertex model or the chiral Potts model or even
three-dimensional Yang-Baxter integrable models become available.Comment: LaTeX2e using iopart.cls, 10 pages, 5 figures (5 eps files), Dunk
Island conference in honor of 60th birthday of A.J. Guttman
Overlapping Unit Cells in 3d Quasicrystal Structure
A 3-dimensional quasiperiodic lattice, with overlapping unit cells and
periodic in one direction, is constructed using grid and projection methods
pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are
the vertices of a convex polytope P, and 4 are interior points also shared with
other neighboring unit cells. Using Kronecker's theorem the frequencies of all
possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final
versio
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
In this paper we show how an infinite system of coupled Toda-type nonlinear
differential equations derived by one of us can be used efficiently to
calculate the time-dependent pair-correlations in the Ising chain in a
transverse field. The results are seen to match extremely well long large-time
asymptotic expansions newly derived here. For our initial conditions we use new
long asymptotic expansions for the equal-time pair correlation functions of the
transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising
model. Using this one can also study the equal-time wavevector-dependent
correlation function of the quantum chain, a.k.a. the q-dependent diagonal
susceptibility in the 2d Ising model, in great detail with very little
computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references
added and minor changes of style. vs3: Corrections made and reference adde
Logarithmic perturbation theory for quasinormal modes
Logarithmic perturbation theory (LPT) is developed and applied to quasinormal
modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is
especially convenient because summation over a complete set of unperturbed
states is not required. Attention is paid to potentials with exponential tails,
and the example of a Poschl-Teller potential is briefly discussed. A numerical
method is developed that handles the exponentially large wavefunctions which
appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st
Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model
In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function
of the square lattice Ising model as a -function of the sixth Painlev\'e
system by constructing an associated isomonodromic system within their theory
of holonomic quantum fields. More recently an alternative isomonodromy theory
was constructed based on bi-orthogonal polynomials on the unit circle with
regular semi-classical weights, for which the diagonal Ising correlations arise
as the leading coefficient of the polynomials specialised appropriately. Here
we demonstrate that the next-to-diagonal correlations of the anisotropic Ising
model are evaluated as one of the elements of this isomonodromic system or
essentially as the Cauchy-Hilbert transform of one of the bi-orthogonal
polynomials.Comment: 11 pages, 1 figur
Increasing atmospheric CO2 concentrations outweighs effects of stand density in determining growth and water use efficiency in Pinus ponderosa of the semi-arid grasslands of Nebraska (U.S.A.)
This study investigated the impacts of environmental (e.g., climate and CO2 level) and ecological (e.g., stand density) factors on the long-term growth and physiology of ponderosa pine (Pinus ponderosa) in a semi-arid north American grassland. We hypothesized that ponderosa pine long-term growth patterns were positively influenced by an increase in atmospheric CO2 concentrations and a decrease in stand density. To test this hypothesis, comparison of long-term trends in tree-ring width and carbon and oxygen stable isotopic composition of trees growing in dense and sparse forest stands were carried out at two sites located in the Nebraska National Forest. Results indicated that tree-ring growth increased over time, more at the sparse than at the dense stands. In addition, the carbon and oxygen isotopic ratios showed long-term increases in intrinsic water use efficiency (WUEi), with little difference between dense and sparse stands. We found a clear trend over time in ponderosa pine tree growth and WUEi, mechanistically linked to long-term changes in global CO2 concentration. The study also highlighted that global factors tend to outweigh local effects of stand density in determining long-term trends in ponderosa pine growth. Finally, we discuss the implications of these results for woody encroachment into grasslands of Nebraska and we underlined how the use of long-term time series is crucial for understanding those ecosystems and to guarantee their conservation
Roots of Unity: Representations of Quantum Groups
Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra
of rank n, are constructed from arbitrary representations of rank n-1 quantum
groups for q a root of unity. Representations which have the maximal dimension
and number of free parameters for irreducible representations arise as special
cases.Comment: 23 page
In memoriam two distinguished participants of the Bregenz Symmetries in Science Symposia: Marcos Moshinsky and Yurii Fedorovich Smirnov
Some particular facets of the numerous works by Marcos Moshinsky and Yurii
Fedorovich Smirnov are presented in these notes. The accent is put on some of
the common interests of Yurii and Marcos in physics, theoretical chemistry, and
mathematical physics. These notes also contain some more personal memories of
Yurii Smirnov.Comment: Submitted for publication in Journal of Physics: Conference Serie
Density Profiles in Random Quantum Spin Chains
We consider random transverse-field Ising spin chains and study the
magnetization and the energy-density profiles by numerically exact calculations
in rather large finite systems (). Using different boundary
conditions (free, fixed and mixed) the numerical data collapse to scaling
functions, which are very accurately described by simple analytic expressions.
The average magnetization profiles satisfy the Fisher-de Gennes scaling
conjecture and the corresponding scaling functions are indistinguishable from
those predicted by conformal invariance.Comment: 4 pages RevTeX, 4 eps-figures include
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