Problem 9. constructing MC simulation of an Einstein solid in Python
The two quantities I tracked throughout this MC simulation were the probability distribution of energies (histogram of energies) and the average energy throughout the simulation (average energy over iterations). Based on the first plot, we can see a very clear decaying exponential relationship for the energy values. This confirms the dependence of the probability distribution of energies on the Boltzmann factor. And for the average energy, we can see that it increases until aroun 1.5. Since beta is set to 1, this matches the 3/2 * kT prediction of the equipartition theorem.