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Related Concept Videos

The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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.
Calculation of First-Law Quantities II01:24

Calculation of First-Law Quantities II

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Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
Entropy02:39

Entropy

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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: Jul 4, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Order parameter statistics in the critical quantum Ising chain.

Austen Lamacraft1, Paul Fendley

  • 1Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714 USA.

Physical Review Letters
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

Researchers found a universal scaling function for magnetization in quantum critical spin systems. This exact solution for the quantum Ising spin chain provides insights into phase transitions.

Related Experiment Videos

Last Updated: Jul 4, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Condensed matter physics
  • Quantum magnetism
  • Statistical mechanics

Background:

  • Phase transitions exhibit universal scaling behavior in the order parameter's probability distribution.
  • At quantum critical points in spin systems, this translates to universal statistics in magnetization distributions of low-lying states.

Purpose of the Study:

  • To determine the exact scaling function for the order parameter distribution at a quantum critical point.
  • To investigate the universal statistics of magnetization in the ground and first excited states of a critical quantum Ising spin chain.

Main Methods:

  • Exact calculation of the scaling function using a connection to the anisotropic Kondo problem.
  • Leveraging the integrability of the quantum Ising spin chain for precise computation.

Main Results:

  • The exact scaling function for the probability distribution of the order parameter was obtained for the ground and first excited states.
  • Demonstrated universal statistics in the total magnetization for the critical quantum Ising spin chain.

Conclusions:

  • The study provides an exact solution for a key aspect of quantum criticality.
  • Confirms the expected universal scaling form of the order parameter distribution at quantum critical points in spin systems.