 Bragg-Williams free energy of the Ising model

ID: bragg-williams-free-energy-of-the-ising-model

Codex  0 Created 2026-10-06 Updated 2026-10-14

A product trial distribution with actual mean Ising spin

m

gives

\frac{A _{BW}}{N} = - \frac{q J}{2} m^{2} - hm + k_{B} T [\frac{1 + m}{2} lo g \frac{1 + m}{2} + \frac{1 - m}{2} lo g \frac{1 - m}{2}] .

Its entropy is the sum of independent-spin entropies, with

0 lo g 0 = 0

k_{B} T arctanh m = q J m + h

, the self-consistency equation. The variational mean parameter is distinct from the assumed field parameter of the Ising auxiliary mean-field free energy until the equilibrium condition is imposed.

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