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Related Concept Videos

Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Paramagnetism01:30

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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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Potential Due to a Magnetized Object01:24

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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
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Atomic Nuclei: Nuclear Relaxation Processes01:23

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Ferromagnetism01:31

Ferromagnetism

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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...
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Diamagnetism01:26

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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.
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Unsupervised Machine Learning Method for the Phase Behavior of the Constant Magnetization Ising Model in Two and

Inhyuk Jang1, Arun Yethiraj1

  • 1Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States.

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|December 26, 2024
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Summary
This summary is machine-generated.

Machine learning now maps phase diagrams for Ising models using local affinity, a novel input feature. This unsupervised approach accurately predicts phase behavior in 2D and 3D systems, including critical exponents.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Machine Learning Applications

Background:

  • Phase transitions are critical phenomena studied using various methods.
  • Machine learning offers unsupervised approaches, avoiding prior assumptions about phase transitions.
  • Previous machine learning studies focused on critical behavior, not off-critical phase diagrams.

Purpose of the Study:

  • To investigate the phase diagram of the Ising model at off-critical magnetizations using machine learning.
  • To develop a robust machine learning method for analyzing phase transitions in 2D and 3D systems.
  • To explore the effectiveness of local affinity as an input feature for machine learning models.

Main Methods:

  • Utilized unsupervised machine learning, specifically a variational autoencoder.
  • Introduced local affinity as a novel input feature, capturing spin and neighbor interactions.
  • Applied the method to the 2D and 3D constant magnetization Ising models.

Main Results:

  • The local affinity feature significantly improved phase behavior prediction accuracy.
  • The variational autoencoder successfully predicted phase diagrams and critical exponent β.
  • Results showed quantitative agreement with conventional simulation methods.

Conclusions:

  • Local affinity is a robust and effective feature for machine learning analysis of phase transitions.
  • The developed unsupervised method accurately characterizes phase diagrams in 2D and 3D Ising models.
  • This approach is generalizable to various lattice and off-lattice systems.