Avergail: Mean Field Theory
Thermodynamics & Statistical Physics arc, page 65 of 193. Back to The Pixelated Physics Universe
Who they are
Avergail has one line, and says it often: “Mean field: i feel the room's average.”
Avergail is a character of the Thermodynamics & Statistical Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Mean-field (Weiss) theory replaces neighbours by their average field; it fails near critical points where fluctuations dominate.
$$ \begin{gathered} B_{\text{eff}} = B + \lambda M \\ \chi = \frac{C}{T - T_c} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $B_{\text{eff}}$ | effective (Weiss mean) field | T |
| $B$ | applied field | T |
| $\lambda$ | molecular-field constant | T·m/A |
| $M$ | magnetisation | A/m |
| $\chi$ | magnetic susceptibility (T > T_c) | — |
| $C$ | Curie constant | K |
| $T$ | temperature | K |
| $T_c$ | Curie temperature | K |
Sources
Crossovers
Avergail meets Taulock (Critical Slowing Down). Avergail's mean field works away from the critical point. Taulock lives at it, where fluctuations grow across all scales and relaxation slows down without limit. That is exactly where mean-field theory fails.
Avergail meets Backrowena (Spontaneous Symmetry Breaking). Backrowena's ground state breaks the symmetry of the Hamiltonian. Avergail's mean-field theory is the simplest place to see it: below the critical temperature, the averaged field picks one direction.
Wear the lore
Concept keywords: Mean Field Theory, Avergail, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics