In the table here we group these configurations according to their total energy and magnetization.
Number spins up | Degeneracy | Energy | Magnetization |
4 | 1 | \( -8J \) | 4 |
3 | 4 | \( 0 \) | 2 |
2 | 4 | \( 0 \) | 0 |
2 | 2 | \( 8J \) | 0 |
1 | 4 | \( 0 \) | -2 |
0 | 1 | \( -8J \) | -4 |