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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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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.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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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.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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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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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.
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NMR Spectroscopy: Spin–Spin Coupling01:08

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Atomic Nuclei: Nuclear Spin State Overview01:03

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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Random Quantum Ising Model with Three-Spin Couplings.

Ferenc Iglói1,2, Yu-Cheng Lin3

  • 1Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary.

Entropy (Basel, Switzerland)
|August 29, 2024
PubMed
Summary
This summary is machine-generated.

This study explores critical properties of a random transverse-field Ising spin chain with multispin interactions using a real-space block renormalization group approach. Results indicate a new universality class for models with three-spin couplings.

Keywords:
critical phenomenadisordered systemsinfinite disorder fixed pointrenormalization group

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Spin Systems

Background:

  • The random transverse-field Ising model is a fundamental model in statistical mechanics.
  • Understanding critical properties and phase transitions is crucial for characterizing materials.
  • Multispin interactions can significantly alter the behavior of quantum spin systems.

Purpose of the Study:

  • To investigate the critical properties of the random transverse-field Ising spin chain with multispin interactions.
  • To analyze the impact of three-spin couplings on the model's phase transitions.
  • To determine if these models belong to a new universality class.

Main Methods:

  • Application of a real-space block renormalization group approach.
  • Analysis of arbitrary block sizes to recover known properties of the two-spin interaction model.
  • Calculation of the critical point for the three-spin coupling model.

Main Results:

  • The renormalization approach successfully reproduced known properties for the two-spin interaction model.
  • The phase transition in the three-spin coupling model is governed by an infinite disorder fixed point.
  • A distinct typical correlation-length critical exponent was identified, differing from the nearest-neighbor coupling model.

Conclusions:

  • The random transverse-field Ising spin chain with three-spin couplings represents a new infinite disorder universality class.
  • Multispin interactions introduce novel critical behavior not observed in simpler models.
  • This research expands the understanding of universality classes in disordered quantum systems.