Phase Transitions and Critical Phenomena

Classify phase transitions as first-order or continuous based on the behavior of free energy derivatives.

Define the concept of an order parameter for various physical systems (e.g., magnets, fluids).

Define the critical exponents (α, β, γ, δ, ν, η) that characterize the singular behavior of observables near a continuous phase transition.

State the scaling hypothesis for the singular part of the free energy and for the correlation function.

Derive the Rushbrooke, Widom, Fisher, and Josephson scaling relations among the critical exponents from the scaling hypothesis.

Explain the concept of universality, where systems with different microscopic details share identical critical exponents.