Thermal Phases, Metastability, and Nucleation

A thermal first-order transition connects equilibrium coexistence to rare nucleation, bubble growth, and eventual conversion of the system. Each step adds physical input: a free-energy barrier alone predicts neither a complete rate nor transition completion.

Enter this chapter

Begin with Landau–Ginzburg Functional Landscapes and Order Parameters to describe phases and interfaces with a coarse-grained free-energy functional.

Helpful background. Convexity, Gauge Dependence, and Physical Phase Criteria and Validity Limits, Thermal Effects, and Gravity develop the definitions used by the chapter’s opening pages.

Topics

1. Landau–Ginzburg Functional Landscapes and Order Parameters — Organizes symmetry, gradients, and order parameters at a specified coarse-graining scale.
2. Thermal Effective Potentials and Phase Diagrams — Constructs perturbative free-energy landscapes and tests their range of validity.
3. Convexity, Gauge Dependence, and Physical Phase Criteria — Distinguishes approximate landscapes from physical thermodynamic phase criteria.
4. Metastability, Spinodals, and Thermal Decay — Separates rare barrier crossing from instability-driven decomposition.
5. Thermal Bounces, Determinants, and Nucleation Rates — Combines critical droplets, fluctuations, and dynamical prefactors into a rate.
6. Bubble Growth and Wall Friction — Connects driving pressure to plasma friction and wall motion.
7. Percolation, Reheating, and Transition Completion — Integrates nucleation and growth through expansion and reheating.
8. Anomalous Charge Violation, Baryogenesis, and Cosmological Interfaces — Identifies the additional transport and cosmological inputs needed for downstream predictions.

How the ideas fit together

A critical droplet is a saddle of a free-energy functional. Its exponential suppression describes the rarity of reaching the barrier, while fluctuations and real-time growth determine the rate prefactor Langer 1969, §§ 2–4. Subsequent wall motion depends on energy–momentum transfer to the surrounding medium.

Consequently, two theories with similar nucleation exponents can complete their transitions differently if their friction or expansion histories differ. Thermodynamic coexistence, nucleation, percolation, and shrinking physical false-phase volume should be tested separately.

Where to go next

Continue to Real-Time Contours, Keldysh Bases, and Response to construct a normalized generating functional for forward and backward evolution.

References

• Langer, J. S. (1969). “Statistical Theory of the Decay of Metastable States.” Annals of Physics 54, 258–275. DOI.