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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Ising spin glasses in dimension five.

P H Lundow1, I A Campbell2

  • 1Department of Mathematics and Mathematical Statistics, Umeå University, Umeå SE-901 87, Sweden.

Physical Review. E
|February 18, 2017
PubMed
Summary
This summary is machine-generated.

Different interaction distributions in five-dimensional Ising spin-glass models create distinct universality classes. Numerical simulations show critical exponents and observables depend on the specific model, confirming model-dependent behavior across dimensions.

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Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Computational physics

Background:

  • Ising spin-glass models are fundamental in understanding complex magnetic phenomena.
  • Previous studies suggested universality in these models, but the role of interaction distribution remained unclear.

Purpose of the Study:

  • To investigate the impact of various interaction distributions (bimodal, Gaussian, uniform, Laplacian) on five-dimensional Ising spin-glass models.
  • To determine if different distributions lead to distinct universality classes.

Main Methods:

  • Detailed numerical simulations were employed to study the models.
  • Data analysis was performed in both finite-size scaling and thermodynamic limit regimes.

Main Results:

  • Critical exponents and dimensionless observables at criticality were found to be model-dependent.
  • Ising spin-glass models with different interaction distributions in five dimensions belong to separate universality classes.

Conclusions:

  • The distribution of interactions significantly influences the universality class of Ising spin-glass models.
  • This finding aligns with observations in two and four dimensions, reinforcing the model-dependent nature of critical parameters.