Midterm 2 Solutions

Problem 1

Consider a magnetic system described by an Ising model $(S_{i}=\pm 1)$ on a square lattice with Failed to parse (syntax error): {\displaystyle H = \sum_i\}

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. 
$Z_{FM}=4$
$Z_{AFM}=4$

b)

Problem 2

a)

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

f) where $T\rightarrow \infty$