Midterm 2 Solutions

Problem 1.

a)

Image of square lattice with ferromagnetic $J_{i,j}<0$ coupling nearest neighbor spins. 
Anti-ferromagnetic $K_{i,j}<0$ coupling only second nearest neighbors. 
$Z_{FM}=4$
$Z_{AFM}=4$

Problem 2.

a)

b) Since Coulomb interactions are long range by $e^{2}/r$ high densities cause the formation of solids such as crystals.