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Related Concept Videos

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...
Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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.
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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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,...

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Related Experiment Video

Updated: Jun 14, 2026

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films
09:32

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Published on: January 26, 2016

Second-order dynamic transition in a p=2 spin-glass model.

Kristina van Duijvendijk1, Robert L Jack, Frédéric van Wijland

  • 1Laboratoire Matière et Systèmes Complexes (CNRS UMR 7057), Université Paris Diderot-Paris, 75205 Paris Cedex 13, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

This study analyzes spin-glass model dynamics using thermodynamic formalism. It reveals a second-order phase transition between active and inactive states in the spin-glass phase.

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Last Updated: Jun 14, 2026

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films
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Published on: January 26, 2016

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Area of Science:

  • Statistical mechanics
  • Complex systems dynamics

Background:

  • Disordered spin models are crucial for understanding complex systems.
  • Ruelle's thermodynamic formalism provides a framework for analyzing dynamical systems.

Purpose of the Study:

  • To analyze the dynamics of a disordered p-spin model (p=2) using Ruelle's thermodynamic formalism.
  • To identify and characterize phase transitions within the dynamical activity of the model.

Main Methods:

  • Application of Ruelle's thermodynamic formalism.
  • Construction of a dynamical Gibbs ensemble using a dynamical activity indicator.
  • Analysis of trajectory dynamics in the low-temperature phase.

Main Results:

  • The dynamics in the spin-glass phase occur at a second-order phase transition.
  • This transition is between dynamically active and inactive trajectories.
  • Similar behavior was observed in a related 3D ferromagnet model.

Conclusions:

  • The study establishes a connection between equilibrium phase transitions and dynamical activity in disordered systems.
  • The findings highlight a universal dynamical behavior across different disordered models.