Two-point correlation functions for a distinguishable particle hopping on a uniform one-dimensional chain

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

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Correlation functions of the one-dimensional random-field Ising model at zero temperature

Physical Review B ◽

10.1103/physrevb.48.9508 ◽

1993 ◽

Vol 48 (13) ◽

pp. 9508-9514 ◽

Cited By ~ 7

Author(s):

Edward Farhi ◽

Sam Gutmann

Keyword(s):

Ising Model ◽

Random Field ◽

Correlation Functions ◽

Zero Temperature ◽

Random Field Ising Model ◽

One Dimensional ◽

The One

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Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3725 ◽

2020 ◽

Author(s):

Naonori S Sugiyama ◽

Shun Saito ◽

Florian Beutler ◽

Hee-Jong Seo

Keyword(s):

Correlation Functions ◽

Hubble Parameter ◽

Theoretical Models ◽

Practical Method ◽

Acoustic Oscillation ◽

Nonlinear Damping ◽

Joint Analysis ◽

Angular Diameter Distance ◽

Point Correlation ◽

Parameter Constraints

Abstract We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform such an analysis with MultiDark Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above 80 h−1 Mpc, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the nonlinear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30\%$ and $20\%$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. This study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modeling of the 3PCF on smaller scales than we consider.

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Correlation functions in finite temperature CFT and black hole singularities

Journal of High Energy Physics ◽

10.1007/jhep06(2021)048 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

D. Rodriguez-Gomez ◽

J.G. Russo

Keyword(s):

Black Hole ◽

Event Horizon ◽

Correlation Functions ◽

Finite Temperature ◽

Proper Time ◽

Black Brane ◽

Point Function ◽

Black Hole Singularity ◽

Point Correlation ◽

Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

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Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Journal of High Energy Physics ◽

10.1007/jhep12(2020)019 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yifei He ◽

Jesper Lykke Jacobsen ◽

Hubert Saleur

Keyword(s):

Potts Model ◽

Correlation Functions ◽

Liouville Theory ◽

Analytical Determination ◽

Conformal Weight ◽

Two Dimensional ◽

Conformal Blocks ◽

Conformal Bootstrap ◽

Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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A new one-dimensional CdIIcoordination polymer with a two-dimensional layered structure incorporating 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole and benzene-1,2-dicarboxylate ligands

Acta Crystallographica Section C Structural Chemistry ◽

10.1107/s2053229616007658 ◽

2016 ◽

Vol 72 (6) ◽

pp. 480-484 ◽

Cited By ~ 2

Author(s):

Qiu-Ying Huang ◽

Xiao-Yi Lin ◽

Xiang-Ru Meng

Keyword(s):

Layered Structure ◽

Room Temperature ◽

Weak Interactions ◽

Coordination Geometry ◽

Dimensional Chain ◽

Two Dimensional ◽

One Dimensional ◽

Heterocyclic Ligand ◽

Rich Variety ◽

Solvent Molecules

The N-heterocyclic ligand 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole (imb) has a rich variety of coordination modes and can lead to polymers with intriguing structures and interesting properties. In the coordination polymercatena-poly[[cadmium(II)-bis[μ-benzene-1,2-dicarboxylato-κ4O1,O1′:O2,O2′]-cadmium(II)-bis{μ-2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole}-κ2N2:N3;κ2N3:N2] dimethylformamide disolvate], {[Cd(C8H4O4)(C11H10N4)]·C3H7NO}n, (I), each CdIIion exhibits an irregular octahedral CdO4N2coordination geometry and is coordinated by four O atoms from two symmetry-related benzene-1,2-dicarboxylate (1,2-bdic2−) ligands and two N atoms from two symmetry-related imb ligands. Two CdIIions are connected by two benzene-1,2-dicarboxylate ligands to generate a binuclear [Cd2(1,2-bdic)2] unit. The binuclear units are further connected into a one-dimensional chain by pairs of bridging imb ligands. These one-dimensional chains are further connected through N—H...O hydrogen bonds and π–π interactions, leading to a two-dimensional layered structure. The dimethylformamide solvent molecules are organized in dimeric pairsviaweak interactions. In addition, the title polymer exhibits good fluorescence properties in the solid state at room temperature.

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The magneto-elastica : from self-buckling to self-assembly

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2013.0609 ◽

2014 ◽

Vol 470 (2162) ◽

pp. 20130609 ◽

Cited By ~ 30

Author(s):

Dominic Vella ◽

Emmanuel du Pontavice ◽

Cameron L. Hall ◽

Alain Goriely

Keyword(s):

Self Assembly ◽

Permanent Magnets ◽

Energy Estimates ◽

Dimensional Chain ◽

Elastic Rod ◽

Straight Chain ◽

One Dimensional ◽

Vibration Dynamics ◽

Magnetic Strength ◽

A Chain

Spherical neodymium–iron–boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.

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