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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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,...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...

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Related Experiment Video

Updated: May 13, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains.

Dmitri A Ivanov1, Alexander G Abanov

  • 1Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 19, 2013
PubMed
Summary

We introduce a new method using full counting statistics to describe correlations in classical and quantum systems. This approach reveals distinct phases in models like the Ising and XY chains, aiding in quantum phase classification.

Related Experiment Videos

Last Updated: May 13, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Area of Science:

  • Statistical Mechanics
  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • Understanding correlations is crucial in both classical and quantum systems.
  • Existing methods may not fully capture the nuances of these correlations.
  • Full counting statistics offers a powerful framework for analyzing discrete observables.

Purpose of the Study:

  • To propose a novel method for describing correlations using full counting statistics.
  • To apply this method to exactly solvable classical and quantum models.
  • To classify quantum phases and analyze phase diagrams.

Main Methods:

  • Utilizing full counting statistics of discrete observables.
  • Applying the method to the classical one-dimensional Ising model.
  • Analyzing the anisotropic spin-1/2 XY chain in a transverse magnetic field.

Main Results:

  • Developed a phase diagram for the 1D Ising model based on Jordan-Wigner strings.
  • Computed full counting statistics of magnetization for the XY chain.
  • Successfully reproduced the known phase diagram for the XY chain, validating the method.

Conclusions:

  • Full counting statistics provides an effective tool for characterizing correlations and phases.
  • The method offers insights into the relationship between different theoretical frameworks, such as Lee-Yang theory.
  • This approach enhances the classification of quantum phases.