6805: 1094 Activities 9

Write your name and answers on this sheet and hand it in at the end.

Ising Model Simulation

Goal: Explore phase transitions and spontaneous symmetry breaking in the 2-D Ising Model

1. From the 6805 home page, go to the webpage for "2-D Ising model (html5)". You will see a grid of blue or yellow squares, which represent up or down spins on a lattice. The controls below let you change the size of the lattice (in each dimension), the temperature, and the monte carlo steps per frame. The system starts at the critical temperature. Move the slider to a high temperature. What are the characteristics of the system at high temperature? Are there any large areas of all blue or all yellow? How large is the magnetization, the net number of up versus down spins (roughly)? Does it look like it is a constant sign?
   
   
   
   
   
   
   
   
2. Now move the slider to the lowest temperature. Does it end up in a uniform ferromagnetic state everywhere? If not, why not? What is the magnetization now? Is this the maximum magnetization possible?
   
   
   
   
   
   
   
   
   
3. Now rapidly bring the temperature to zero and let it settle down. Repeat the cycle of rapid heating and cooling several times. Does it always end up in a uniform ferromagnetic state? If not, why not? Estimate the magnetization per spin in each case.
   
   
   
   
   
   
   
   
4. Next change the temperature by increments of about 1 (you have to release the slide for the change to take affect). Characterize the behavior of the system as it heats through the critical temperature to high temperature. What happens at 2.27 (restart the page to get there exactly)? Make a sketch of the magnetization as a function of temperature.
   
   
   
   
   
   
   
   
5. Play with changing the cell size (by the Size pull down) to very large and very small. What differences do you observe in the size of the fluctuations and the behavior of the magnetization?
   
   
   
   
   
   
   
   

Discussion questions on QCD stuff, part 1

Goal: Review some of the physics of quantum chromodynamics discussed in the slides and videos.

1. In your own words, what is the origin of the mass of proton (or most of it)?
   
   
   
   
   
   
   
   
2. We draw field lines to represent electric fields. Draw what they look like for a positron and an electron at a fixed distance. How do the field lines show that the force decrease between them with increasing distance?
   
   
   
   
   
   
   
   
   
3. We can draw field lines for color ("chromo-electric") fields as well. Draw what they look like for a quark and an anti-quark at a fixed distance. How do the field lines show that the force is constant with increasing distance?
   
   
   
   
   
   
   
   
   
4. Why does a constant force imply a linearly increasing potential (or linearly increasing energy in the fields) with increasing distance?