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Related Concept Videos

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,...
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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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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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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
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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

Optimizing glassy p-spin models.

Creighton K Thomas1, Helmut G Katzgraber

  • 1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 24, 2011
PubMed
Summary
This summary is machine-generated.

Computing the ground state for p-spin Ising models is NP-hard, even in two dimensions for p=3. This study introduces algorithms to find these ground states for large systems with high confidence.

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Area of Science:

  • Computational physics
  • Statistical mechanics
  • Complexity theory

Background:

  • Ising spin-glass models are fundamental in statistical mechanics.
  • Determining the ground state (lowest energy configuration) is often computationally intractable.
  • Standard two-spin interactions are well-studied, but p-spin interactions introduce greater complexity.

Purpose of the Study:

  • To investigate the computational complexity of ground state determination for p-spin Ising models.
  • To specifically analyze the case of three-spin (p=3) interactions in two spatial dimensions.
  • To develop and present algorithms for efficiently finding approximate ground states of p-spin models.

Main Methods:

  • Complexity analysis to establish the NP-hard nature of the problem.
  • Development of generic exact algorithms for ground state computation.
  • Implementation of heuristic algorithms for large-scale systems.
  • Validation of algorithms for systems up to several thousand spins.

Main Results:

  • Computing the ground state for p-spin Ising models is NP-hard in general.
  • For p=3, the problem remains NP-hard even in two spatial dimensions, unlike the two-spin case.
  • The proposed algorithms achieve high confidence in finding ground states for large systems.

Conclusions:

  • The computational difficulty of Ising spin-glass ground states increases significantly with higher-order interactions (p>2).
  • The developed algorithms provide practical tools for tackling complex p-spin models in physics and computer science.
  • This work advances the understanding of complexity in disordered magnetic systems.