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Phase transitions and critical phenomena
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Module 10
The Epsilon Expansion
1
The $\epsilon$-Expansion: Perturbation Around the Upper Critical Dimension
Explain the logic of the ε-expansion as a controlled perturbative expansion around the upper critical dimension d=4.
2
Critical Exponents η and γ to First Order in ε
Calculate the critical exponents η and γ to first order in ε.
3
Comparing ε-Expansion Predictions with 3D Ising Model Simulations
Compare the predictions of the ε-expansion for d=3 with numerical results for the 3D Ising model.
4
RG and Crossover Phenomena
Describe how the RG framework explains crossover phenomena between different critical behaviors.
5
From φ⁴ to O(n): Describing Multi-Component Order Parameters
Generalize the φ⁴ theory to the O(n) model to describe systems with n-component order parameters.
6
Key Results for Special Limits of the O(n) Model
State the key results for special limits of the O(n) model, such as the self-avoiding walk (n→0) and the spherical model (n→∞).
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Momentum-Space Renormalization Group
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Advanced Topics in Critical Phenomena