Construct a Metropolis Monte Carlo code for a two-dimensional Ising magnet with 20 x 20 = 400 Spins and periodic boundary conditions. Run the code and collect statistics from the trajectory to analyze...

Construct a Metropolis Monte Carlo code for a two-dimensional Ising magnet with 20 x 20 = 400 Spins and periodic boundary conditions. Run the code and collect statistics from the trajectory to analyze the spin statistics. In particular, compute

And for various separations between spins
i
and
j, compute the correlation function

where
is over all pairs of spins in the lattice for which l and m are separated by the same distance as
i
and
j, and n_ij
is the total number of such pairs in the lattice. Perform these calculations for temperatures both above and below the critical point. Try to demonstrate the existence of long range correla-tions near the critical point and spontaneous symmetry break-ing below the critical temperature.