Optional Project 2: Ising Model Simulation (3 possible quiz grades)
-Write a computer program that simulates the Ising Model (2D) using the Metropolis method described at http://ace.acadiau.ca/science/phys/ising/. (quiz grade 1)
-Try your code on 10/10 2D matrix then on a 100/100 matrix for various temperatures 0, 0.1, 0.2, 1 (find the critical temperature). (quiz grade 1)
-Modify the program for simulation of a 3D model using the same approach and a 10x10x10 matrix for the same temperatures. Find the critical temperature and compare this with the 2D critical temperature. (quiz grade 2)
-Modify the program for a 1-d simulation of a polymer chain (polyethylene)
using the 3 rotational isomeric states to generate the lowest
energy chain conformation for a chain of length N. Find the critical temperature
for a planar zig-zag conformation. This is the simulated crystallization
temperature. (quiz grade 3) India Notes with Ising model for chain, helpful notes.
Plot fraction trans versus temperature on a semi-log scale (log temperature) to determine the critical temperature.
-Modify the program for a 1-d simulation of a polymer chain (polyethylene)
using the 9 rotational isomeric states for dimers to generate the lowest
energy chain conformation for a chain of length N. Find the critical temperature
for a planar zig-zag conformation. This is the simulated crystallization
temperature. (quiz grade 4) India Notes with Ising model for chain, helpful notes.
Plot fraction trans versus temperature on a semi-log scale (log temperature) to determine the critical temperature.
Possible approach:
Also See: http://bartok.ucsc.edu/peter/java/ising/ising.html
Figure 1 showing results using the above routine for the Ising Metropolis simulation. Random start, T = 1, T = 0.2, T = 0.1, T = 0. 5000 steps, 50x50 grid.