Curie-Weiss Mean-Field Ferromagnet

Order parameter, free energy landscape, and phase diagram

Parameters

Tc = 1.00 (J=1, k_B=1)

Observables

Magnetization m*
Susceptibility χ
Free energy F*
T/Tc
Phase

Theory

The Curie-Weiss self-consistency equation:

m = tanh((Jzm + H) / T)

The Landau free energy f(m) = −Jzm²/2 − Hm + T·[(1+m)ln(1+m)+(1−m)ln(1−m)]/2. Below Tc = Jz, spontaneous magnetization appears via pitchfork bifurcation. The lower panel shows m*(T) at H=0.