Magnetization

Section 1 Exercises:

1. Run the applet with an initial temperature of T = 5.0 and no external magnetic field.  Watch the magnetization for about 15 seconds and pause the applet.   Give an estimate for the average magnetization for this temperature.  Also estimate the standard error.
2. Observe the behavior of the magnetization for the temperatures 6.0, 7.0, 8.0, and 9.0.  Describe any changes in behavior compared to your answer for Exercise 1?
3. Describe the behavior of the spin lattice and the magnetization plot for T = 1. (Hint: domains)
4. There is a critical temperature below which a permanent magnetization appears.  What is it?  (Hint:  It's not an easy transition to detect.  You may have to wait a while to see a trend in the magnetization.)
5. Choose a low temperature such as T = 0.1 and H = 0.  Do the simulation several times starting from different initial conditions.  The Reset button will give a different random starting distribution.  Is the final magnetization the same?  Is the final preferred direction always the same?  Discuss your conclusions.
6. Reset the applet and Clear the graph.  Set the temperature to T = 7.0.  Turn on the magnetic field to H = 0.1.  What effect does this have on the magnetization?  Record the average value of the magnetization.
7. Increase the magnetic field to 0.2, 0.5, 1.0, 2.0, 5.0 and 10.0.   Record the final average value of the magnetization for each field.  Make a plot of your data.  Describe the functionality of this plot.
8. Change the temperature to T = 1 and H = 0.  Let the system evolve for a few seconds and observe the behavior.  Pause the system and set H = 0.1.  Run the system and describe what happens.  Is this the same behavior you saw in Exercises 6 & 7?