Phase Transitions

2D Ising model — ferromagnetic order and critical phenomena at T_c ≈ 2.27

Temperature

T / J·k_B⁻¹ 2.3

External field H 0.0

Steps/frame 3

Magnetization ⟨m⟩: —

Energy ⟨E⟩: —

T_c (exact): 2.269

Phase: —

The Ising model on a 2D square lattice has an exact solution (Onsager 1944): T_c = 2J/(k_B ln(1+√2)) ≈ 2.269.

Below T_c: long-range order, magnetized domains. Above T_c: disordered paramagnetic phase. Near T_c: scale-free fluctuations and critical exponents.

Right: magnetization vs. temperature measured during sweep.