Classification of Phase Transitions

Phase transitions are sorted by how thermodynamic quantities behave at the transition, the principal divide being between first-order transitions with latent heat and continuous transitions without it.

Definition

The classification of phase transitions organizes them by the analytic behavior of the free energy at the transition: first-order transitions show a discontinuity in its first derivatives with latent heat, while continuous transitions have continuous first derivatives but singular higher derivatives.

Scope

This topic covers the distinction between first-order transitions, marked by a discontinuity in first derivatives of the free energy and an associated latent heat, and continuous (second-order) transitions, where first derivatives are continuous but higher derivatives diverge or jump. Coexistence, metastability and hysteresis, phase diagrams and the critical point, and the Ehrenfest classification and its limitations are included.

Core questions

• How does the behavior of free-energy derivatives distinguish first-order from continuous transitions?
• Why do first-order transitions involve latent heat, metastability, and hysteresis?
• What happens to the distinction between phases at a critical point?
• What are the limitations of the original Ehrenfest classification scheme?

Key concepts

• First-order transitions and latent heat
• Continuous (second-order) transitions
• Phase coexistence and critical point
• Metastability and hysteresis
• Ehrenfest classification and its limits

Clinical relevance

Distinguishing the order of a transition matters for understanding melting, boiling, and sublimation, the magnetic and superconducting transitions, and engineering processes from crystallization to alloy formation, where latent heat and hysteresis have practical consequences.

History

Ehrenfest proposed classifying transitions by the lowest discontinuous derivative of the free energy in the 1930s; the scheme was later refined into the modern first-order versus continuous distinction once divergences, rather than simple jumps, were recognized at critical points.

Key figures

• Paul Ehrenfest
• Lev Landau

Seminal works

• landaulifshitz1980stat
• stanley1971

Frequently asked questions

Why is melting first-order but the Curie transition continuous?

Melting absorbs latent heat and shows a discontinuous density change, the signatures of a first-order transition, whereas a ferromagnet's magnetization falls continuously to zero at the Curie point with no latent heat, the hallmark of a continuous transition.