Monte Carlo simulation of a d = 2 Ising model

Write a computer program to perform a Monte Carlo computer simulation of the two-dimensional Ising model in zero magnetic field.

where the sum is over nearest-neighbor pairs of sites on a square lattice

1. Write a program to perform a Monte Carlo simulation of the two-dimensional Ising model. You should be able to simulate any size L × L lattice, with L determined at the beginning of the program. You should be able to set the temperature J at the beginning of the program. You can also write the program for zero magnetic field. (We will use non-zero fields in later problems.)

2. Beginning with a random configuration on a fairly large lattice (L = 32), perform a single run of 20 MC sweeps at T = 5.0. and look at the printout of the configuration.

3. Beginning with a random configuration on a fairly large lattice (L = 32), perform a single run of 20 MC sweeps at T = 3.0. and look at the print-out of the configuration.

4. Beginning with a random configuration on a fairly large lattice (L = 32), perform a single run of 20 MC sweeps at T = 2.0, and look at the print-out of the configuration.

5. Compare the pictures of the configurations that you have generated at T = 5.0, 2.0, 2.0. What do you see?

6. Beginning with a random configuration on a fairly large lattice (L = 16 or L = 32), perform several runs with about 50 or 100 MC sweeps at T = 0.5. Keep the length of the runs short enough so that you can do it several times without wasting your time. Look at the print-outs of several configurations. If you see something that seems unusual, print it out and hand it in. Explain why you think it unusual.