Ising Mean-Field Transition

Bifurcation of magnetization at the critical temperature T_c = Jz/k_B

Phase diagram: m vs T
Convergence: m(t) → fixed point
T_c = 4.00 T/T_c = 0.50 m* = 0.000 Phase: Ordered
About: The mean-field Ising model replaces interactions with an effective field. Magnetization satisfies the self-consistency equation m = tanh(βJzm). Below T_c = Jz/k_B a non-zero solution exists — spontaneous symmetry breaking. The bifurcation diagram shows the pitchfork bifurcation at T_c, the hallmark of second-order phase transitions.