Generalized difference equation for the three-dimensional Ising ferromagnet

1984 ◽  
Vol 62 (1) ◽  
pp. 35-39 ◽  
Author(s):  
B. Frank ◽  
C. Y. Cheung
Keyword(s):  
Difference Equation ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Ferromagnetic Transition ◽  
Nearest Neighbour ◽  
Ising Ferromagnet ◽  
Cubic Lattices ◽  
Self Consistent ◽  
The Difference ◽  
Single Relation

The difference equation method of Frank, Cheung, and Mouritsen (FCM) is made self-consistent by relaxing an assumption of the theory which pertains to the correlation of a spin with its nearest neighbour. The full set of A = 1 and I − δ equations and U equations is brought into play, with the U2 = T2 = (1/4) (1 − 1/F(1)) double equation replaced by a single relation between U2 and T2. The resulting ferromagnetic transition temperatures for the cubic lattices are consistent with the series results to within about 2%. The correlation functions are much closer to the series results than those of FCM.

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

1972 ◽  
Vol 9 (01) ◽  
pp. 76-86
Author(s):  
M. S. Bartlett
Keyword(s):  
Time Series ◽  
Correlation Functions ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Correlations ◽  
Orthogonal Expansions ◽  
Non Linear ◽  
Time Series Approach

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed. Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.

Monte Carlo Renormalization of the 3-D-Ising Model and the Analyticity of Block-Spin Transformations

1991 ◽  
Vol 02 (01) ◽  
pp. 487-490 ◽  
Author(s):  
T.S. SMIT ◽  
J.R. HERINGA ◽  
H.W.J. BLÖTE ◽  
A. COMPAGNER ◽  
Y.T.J.C. FONK ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Correlation Functions ◽  
Coupling Constants ◽  
Nearest Neighbour ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Lattice Size ◽  
The Stability ◽  
Derivatives Of ◽  
Monte Carlo Renormalization Group

We present a new analysis on Monte Carlo Renormalization Group (MCRG) results obtained earlier by means of the Delft Ising System Processor (DISP). The MCRG data involve a total of 57 coupling constants, 36 even and 21 odd. Simulations were carried out for simple cubic lattices with 643, 323 and 163 spins. The RG transformation is assumed to be analytic. A number of relations exist between correlation functions at different renormalization levels. Some of these involve the derivatives of the stability matrix. These correlation functions enable an analysis of the so-called regular part of the RG transformation. If the Hamiltonian of the original lattice only contains nearest-neighbour couplings then the regular contributions to the specific heat and the magnetic susceptibility can be easily determined. These contributions must depend only weakly on the initial lattice size, at least if the RG transformation is analytic. We investigated whether this is indeed true when the majority-rule is applied. New simulations involving higher-order correlations will enable us to study the analytic contributions in more detail.

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

1972 ◽  
Vol 9 (1) ◽  
pp. 76-86 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Time Series ◽  
Correlation Functions ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Correlations ◽  
Orthogonal Expansions ◽  
Non Linear ◽  
Time Series Approach

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed.Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.

Defocus ramp correction in spot-scan imaging

1992 ◽  
Vol 50 (1) ◽  
pp. 130-131
Author(s):  
Kenneth H. Downing
Keyword(s):  
Computer Control ◽  
Three Dimensional ◽  
Sufficient Accuracy ◽  
Objective Lens ◽  
Electron Crystallography ◽  
Contrast Transfer Function ◽  
Tilt Axis ◽  
Specimen Height ◽  
The Difference ◽  
Envelope Functions

Three-dimensional structures of a number of samples have been determined by electron crystallography. The procedures used in this work include recording images of fairly large areas of a specimen at high tilt angles. There is then a large defocus ramp across the image, and parts of the image are far out of focus. In the regions where the defocus is large, the contrast transfer function (CTF) varies rapidly across the image, especially at high resolution. Not only is the CTF then difficult to determine with sufficient accuracy to correct properly, but the image contrast is reduced by envelope functions which tend toward a low value at high defocus.We have combined computer control of the electron microscope with spot-scan imaging in order to eliminate most of the defocus ramp and its effects in the images of tilted specimens. In recording the spot-scan image, the beam is scanned along rows that are parallel to the tilt axis, so that along each row of spots the focus is constant. Between scan rows, the objective lens current is changed to correct for the difference in specimen height from one scan to the next.

The iron content of iron superoxide dismutase: determination by anomalous scattering

1983 ◽  
Vol 218 (1210) ◽  
pp. 119-126 ◽  
Keyword(s):  
Superoxide Dismutase ◽  
Iron Content ◽  
Three Dimensional ◽  
Anomalous Scattering ◽  
Total Iron Content ◽  
Iron Site ◽  
Iron Superoxide Dismutase ◽  
Density Map ◽  
The Difference ◽  
Electron Density Map

The number of iron atoms in the dimeric iron-containing superoxide dismutase from Pseudomonas ovalis and their atomic positions have been determined directly from anomalous scattering measurements on crystals of the native enzyme. To resolve the long-standing question of the total amount of iron per molecule for this class of dismutase, the occupancy of each site was refined against the measured Bijvoet differences. The enzyme is a symmetrical dimer with one iron site in each subunit. The iron position is 9 ņ from the intersubunit interface. The total iron content of the dimer is 1.2±0.2 moles per mole of protein. This is divided between the subunits in the ratio 0.65:0.55; the difference between them is probably not significant. Since each subunit contains, on average, slightly more than half an iron atom we conclude that the normal state of this enzyme is two iron atoms per dimer but that some of the metal is lost during purification of the protein. Although the crystals are obviously a mixture of holo- and apo-enzymes, the 2.9 Å electron density map is uniformly clean, even at the iron site. We conclude that the three-dimensional structures of the iron-bound enzyme and the apoenzyme are identical.

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

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