Thermal Phases, Metastability, and Nucleation
A thermal first-order transition is not one calculation but a chain of distinct claims. A nonconvex coarse-grained landscape suggests candidate phases; a physical phase criterion identifies coexistence; a saddle supplies an exponential suppression; determinants and real-time growth supply a rate; wall and hydrodynamic dynamics supply bubble growth; and a history integral decides percolation and completion. No earlier link alone proves a later one.
Enter this chapter
Section titled “Enter this chapter”Landau–Ginzburg functionals organize symmetries, order parameters, gradients, and interfaces at a declared coarse-graining scale. Thermal effective potentials construct perturbative phase-diagram tools, while convexity and gauge-invariant criteria separate those tools from physical thermodynamic statements.
The dynamical sequence begins with metastability and spinodals. Thermal bounces and rates distinguish the Euclidean exponent from zero modes, determinants, statistical normalization, and a real-time growth prefactor. Wall friction then determines whether bubbles accelerate, reach a terminal velocity, or become hydrodynamically unstable. Percolation and completion integrate the rate and growth law through expansion and reheating. The final anomaly and cosmology interface states which thermal-QFT outputs can enter baryogenesis or cosmological calculations without importing their conclusions.
| Claim | Required object | Decisive failure test |
|---|---|---|
| Candidate phases | Symmetry-complete coarse-grained functional | Change the coarse-graining scale and include omitted invariants or gradients. |
| Physical coexistence | Gauge-invariant free energies or operator criteria | Test gauge, scale, volume, and branch dependence consistently. |
| Nucleation rate | Saddle, one negative mode, zero-mode measure, determinant, and dynamical prefactor | Check O(3)/O(4), EFT power counting, double counting, and dilute-bubble control. |
| Bubble growth | Wall–plasma matching and friction closure | Resolve all hydrodynamic branches and their stability. |
| Completion | History-dependent false-phase fraction | Include reheating and demand shrinking physical false-phase volume. |
| Downstream signal | Transition outputs plus a separate transport or cosmological model | Propagate uncertainties and forbid conclusions stronger than the exported inputs. |
Conventions and boundaries
Section titled “Conventions and boundaries”The volume uses the metric. Thermal free-energy densities are denoted or only after the effective object is identified. The Euclidean actions and have dimensions one and zero respectively in natural units; the suppressions are and . A bounce exponent is never called a rate.
Figures registered for this chapter are not required to understand the exposition: every spatial or process relation is also stated mathematically. Quantitative phenomenology remains conditional on a declared theory, parameters, renormalization prescription, cosmological history, and current rate inputs.