Skip to main content
grasp.study
About
Explore
Pricing
Log in
Try it for free
Back to course
👋
Welcome to a Grasp lesson
Create a free account
to keep studying and create your own study path.
Foundations of Statistical Mechanics
·
Module 12
Landau Theory of Phase Transitions
1
Landau Free Energy: A Symmetry-Constrained Expansion
Construct the Landau free energy as a symmetry-constrained polynomial expansion in the order parameter near a phase transition.
2
Landau Theory and Mean-Field Critical Exponents
Show that minimizing the Landau free energy reproduces the mean-field critical exponents for a continuous transition.
3
Landau Theory and First-Order Phase Transitions
Model a first-order phase transition within Landau theory by including higher-order terms in the expansion.
4
Superfluid Helium-4: A Landau Theory Approach
Apply Landau theory to describe the superfluid transition in Helium-4 using a complex order parameter.
5
From Landau-Ginzburg to Free Energy: Exploring Spatial Variations
Introduce spatial variations of the order parameter to construct the Landau-Ginzburg free energy functional.
6
Ornstein-Zernike Correlation from Landau-Ginzburg
Derive the Ornstein-Zernike form of the correlation function and the behavior of the correlation length from the Landau-Ginzburg functional.
7
Ginzburg Criterion: Validating Mean-Field Theory
Derive the Ginzburg criterion to determine the temperature range where mean-field theory is valid by comparing fluctuation contributions to mean-field values.
8
From Landau to Renormalization: Understanding Critical Phenomena
Explain how the breakdown of Landau theory near the critical point motivates the need for the Renormalization Group.
End of course,
Back to course
Previous module
Phase Transitions and Critical Phenomena
Next module