Magnetic order in insulators Antiferromagnetic order ↑↓↑↓↑↓↑ Ferromagnetic order ↑↑↑↑↑↑↑ · Heisenberg model H=1S, 1>0 Antiferromagnetic 1<0 Ferromagnetic• Antiferromagnetic order • Ferromagnetic order • Heisenberg model I > 0 Antiferromagnetic I < 0 Ferromagnetic Magnetic order in insulators