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Related Concept Videos

Ferromagnetism01:31

Ferromagnetism

Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic dipoles are rigidly aligned in the same direction within a domain by quantum mechanical coupling among the atoms. This coupling is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. However, some materials have weaker coupling, and are ferromagnetic at lower...
Valence Bond Theory02:42

Valence Bond Theory

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...
Magnetic Fields01:27

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...
Diamagnetism01:26

Diamagnetism

Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
Colors and Magnetism03:02

Colors and Magnetism

Color in Coordination Complexes
When atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the d orbitals often allows photons in the visible range to be absorbed and emitted, which is seen as colors by the human eye.
Paramagnetism01:30

Paramagnetism

Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...

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Related Experiment Video

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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
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Antiferromagnetic Ising model in small-world networks.

Carlos P Herrero1

  • 1Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, Campus de Cantoblanco, 28049 Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

Disorder in antiferromagnetic Ising models on small-world networks induces a spin-glass phase. Increasing disorder lowers the transition temperature, which saturates at approximately 1.7 J, revealing insights into spin-glass behavior.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Network Science

Background:

  • The antiferromagnetic Ising model is a fundamental model in statistical mechanics.
  • Small-world networks exhibit unique topological properties, bridging regular and random networks.
  • Disorder and frustration are key concepts in understanding complex magnetic phases like spin glasses.

Purpose of the Study:

  • To investigate the impact of disorder on the antiferromagnetic Ising model within small-world networks.
  • To characterize the paramagnetic to spin-glass phase transition as a function of network disorder.
  • To determine the relationship between rewiring probability and transition temperature.

Main Methods:

  • Utilizing Monte Carlo simulations to model the system's behavior.
  • Generating small-world networks from two-dimensional regular lattices with varying rewiring probabilities (p).
  • Analyzing the paramagnetic to spin-glass transition temperature (Tc) and system energy.

Main Results:

  • The introduction of long-range connections (disorder) leads to frustration and a spin-glass phase at low temperatures.
  • Transition temperature (Tc) decreases with increasing disorder (p).
  • Tc saturates to approximately 1.7 J for p > 0.4, where J is the antiferromagnetic coupling.
  • Energy increases linearly with p at small p and low temperatures.
  • In the strong-disorder limit (p → 1), the model becomes equivalent to a short-range +/-J spin glass on random networks.

Conclusions:

  • Disorder-induced frustration is crucial for the emergence of the spin-glass phase in this model.
  • The small-world network structure significantly influences the magnetic phase transitions.
  • The study provides a bridge between ordered lattice models and disordered spin-glass models.