Monte Carlo simulation of the square-lattice Ising model with the exact Onsager solution overlaid. Critical temperature k_BT_c/J = 2/ln(1+√2) ≈ 2.269. The specific heat diverges logarithmically at T_c.
Temperature T/T_c = 1.00
External Field h = 0.00
Metropolis algorithm. White=↑, Black=↓. Red dot = current state. Blue curve = Onsager exact magnetization |m|=(1−sinh(2J/kT)^{-4})^{1/8}.