Introduction to the Theory of Ferromagnetism

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Английский
14 h
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  • From www.edx.org
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  • Self-paced
  • Free Access
  • Fee-based Certificate
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  • 7 Sequences
  • Intermediate Level

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Course details

Syllabus

First week

  • Opening lecture. Classification of phase transitions

Second week

  • Atomic magnetic moment
  • Physical quantities characterizing the magnetic properties of matter
  • Classification of materials for their magnetic properties

Third week

  • Isolated local magnetic moment in an external magnetic field
  • A system of noninteracting local magnetic moments in an external magnetic field
  • Curie law
  • Effective Weiss field
  • Exchange interaction
  • Interaction of two local magnetic moments

Fourth week

  • Heisenberg model and Ising model
  • Mean-field approximation in the Ising model
  • Curie-Weiss equation and Curie-Weiss law
  • Ferromagnetic transition in the Ising model. Curie temperature. Order parameter
  • Temperature dependence of the ferromagnetic order parameter in the Ising model
  • Ground and excited states of a ferromagnet in the Ising model

Fifth week

  • Free energy of a ferromagnet in the Ising model. Free energy of a ferromagnet near the critical temperature
  • Spontaneous symmetry breaking at the paramagnetic-ferromagnetic transition
  • Phenomenological Landau theory of second-order phase transitions
  • Heat capacity and magnetic susceptibility of the Ising ferromagnet in the mean-field approximation
  • Critical exponents

Sixth week

  • Exact solution of the Ising model in one dimension
  • Ising model for antiferromagnets. Mean-field approximation. Neél temperature
  • Magnetic susceptibility of the Ising antiferromagnet in the mean-field approximation

Seventh week

  • Problems solving. Concluding remarks

Prerequisite

Basic knowledge of vector calculus, theory of functions of a complex variable, theory of differential equations, probability theory, statistical physics, and quantum mechanics is required.

Instructors

Mikhail Maslov
Associate Professor at Department of Condensed Matter Physics, National Research Nuclear University MEPhI, PhD
National Research Nuclear University

Editor

National Research Nuclear University “MEPhI” is one of the most recognized technical universities in Russia. It is the only research nuclear university in Russia. The aim of the university existence is preparing the specialists for nuclear industry, science, information technology and other high-tech sectors of Russian economy. National Research Nuclear University “MEPhI” implements postgraduate professional education curricula (PhD and postdoctoral level), carries out fundamental and applied scientific research in high-priority fields of science and technologies. Among MEPhI graduates are Nobel Prize winners, members of the Russian Academy of Sciences, and winners of national prizes. Its professors and alumni have made major contributions to various fields of theoretical and experimental physics, mathematics, cybernetics, and computer sciences.

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