This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Major Project: Ising Model PHZ 5156 This problem combines what we have learned about the technique of MonteCarlo simulation with the physics of magnetic phase transitions. In a magnetic material (e.g. Ni, Fe, etc.) at high temperatures, each atom has a large local magnetic moment, but they tend to be unaligned. By contrast, at low temperatures, exchange interactions tend to align the spins and create a macroscopic magnetic moment. We will make a simple model of the interactions and then use statistical physics to describe the phase transition from the paramagnetic to ferromagnetic state. The Hamiltonian H for a twodimensional spin system is given by H = 1 2 J N X i =1 N X j =1 S ij ( S i +1 ,j + S i 1 ,j + S i,j +1 + S i,j 1 ) (1) We can also consider adding an applied external field H which adds a term to the Hamiltonian H N i =1 N j =1 S ij . A more shorthand way to write this is H = J X h ij i S i S j H X i S i (2) where the summation is over nearest neighbor spins and H is an externally applied field....
View
Full
Document
This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.
 Fall '08
 Johnson,M

Click to edit the document details