** HW 5.1(a):**

I have ran the code for simulated annealing with the Lennard Jones potential.

When i started from a square lattice with seed number 10001 at the temperature of 1200 and 35000 number of runs i got a defect free triangular lattice, see figure 1. At a lower number of steps or different temperature it was not a defect free triangular lattice.

Figure 1

When i started from a random lattice with seed number 10001, at the temperature of 1150 and 56000 number of runs i got a defect free triangular lattice, see figure 2. At a lower number of steps or different temperature it was not a defect free triangular lattice.

Figure 2

If i raise the temperature (to the one i began with) again after cooling for a while, the lattice will stay the same. But if i raise the temperature even more, the defect free triangular lattice 'gets out of control' and there is no apparent order, see figure 3.

Figure 3

If i quench the sample immediately, the lattice does not change.