Physics / advanced
Order, fluctuations, and critical scaling
Move from symmetry and mean-field order to scaling, renormalization flows, and the quantitative limits of approximation near phase transitions.
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Module 01 advanced
Order, fluctuations, and critical scaling
Move from symmetry and mean-field order to scaling, renormalization flows, and the quantitative limits of approximation near phase transitions.
- 01
Order parameters and symmetry-breaking patterns
Identify which observable distinguishes ordered phases and explain how symmetry selection differs between finite systems and thermodynamic limits.
32 min - 02
Landau free energy and first-order transitions
Use symmetry-constrained local free-energy expansions to distinguish equilibrium coexistence, metastable branches, and mean-field spinodals.
32 min - 03
Ginzburg criterion and fluctuation dominance
Estimate when fluctuations invalidate a uniform saddle point and connect that comparison to a correctly normalized susceptibility.
32 min - 04
Ising transfer matrix in one dimension
Solve the finite periodic nearest-neighbour Ising chain and extract its analytic free energy, correlation length, and zero-field susceptibility.
32 min - 05
Correlation length and scaling hypotheses
Define critical exponents on specified paths and derive relations only after identifying the homogeneity and correlation assumptions they require.
32 min - 06
Real-space renormalization examples
Perform an exact zero-field Ising-chain decimation and distinguish preserved long-distance physics from lost microscopic information.
32 min - 07
Momentum-shell renormalization for scalar models
Integrate short-wavelength fluctuations, restore the cutoff by rescaling, and track convention-dependent one-loop scalar couplings.
32 min - 08
Wilson–Fisher fixed-point calculation
Find the interacting scalar fixed point near four dimensions and extract exponents consistently to first order in epsilon.
32 min - 09
Kosterlitz–Thouless vortex unbinding
Explain how compact phase defects produce a two-dimensional transition without ordinary magnetization and derive its characteristic vortex-flow diagnostics.
32 min - 10
Finite-size scaling and data collapse
Use sample size as a controlled infrared cutoff and assess whether rescaled observations support a stated critical scaling hypothesis.
32 min