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Phase transitions and critical phenomena
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Module 4
Mean-Field Theory of Magnetism
1
Mean-Field Theory of the Ising Model
Derive the mean-field equation for the Ising model using the molecular field approximation.
2
Magnetization Near the Critical Point: Graphical and Analytical Solutions
Solve the self-consistency equation for magnetization graphically and analytically near the critical point.
3
Mean-Field Critical Exponents of the Ising Model
Calculate the full set of mean-field critical exponents (α, β, γ, δ) for the Ising model.
4
Mean-Field Free Energy: Variational Approach
Derive the mean-field free energy using the Bogoliubov inequality (variational principle).
5
Mean-Field Theory for the Classical Heisenberg Model
Apply mean-field theory to the classical Heisenberg model and compare its predictions with the Ising case.
6
Fluctuations, Dimensionality, and Mean-Field Theory Breakdown
Qualitatively discuss the role of fluctuations and dimensionality in the breakdown of mean-field theory.
Previous module
The Ising Model and Exact Solutions
Next module
Landau Theory of Phase Transitions