Physics / Math
Ising model
A ferromagnet's phase transition: domains and critical temperature.
What happens
A grid of tiny magnets that only talk to their neighbours, yet together they know how to freeze: cold, they lock into large domains; hot, they flicker at random; and right at the critical temperature fluctuations of every size coexist. Sweep the temperature across the transition and watch the magnetization chart.
Equations used in the module
Equations E = −J Σ s_i s_j (h = 0, J = k = 1) P(flip) = min(1, exp(−ΔE / kT)) (Metropolis) T_c = 2 J / (k ln(1 + √2)) ≈ 2.269 J/k
