PHYS 445 Lecture 32  Ising model
32  1
© 2001 by David Boal, Simon Fraser University.
All rights reserved; further resale or copying is strictly prohibited.
Lecture 32  Ising model
What's Important:
•
Ising model in 3D
Text
: Reif
Ising model
In the previous lecture, we considered the effects of dimensionality on the existence of
phase transitions, using a spin system as an example. Let's now examine the
properties of this system, which is called the Ising model, in three dimensions.
Comments:
•
The Ising model in two dimensions has been solved exactly by Onsager, although
the proof is difficult.
•
Reif also considers systems subject to magnetic fields, and extends the results here
for spin  1/2 to systems with general spin
S
.
One form often used to represent the interaction energy between two objects with spin
vectors
S
j
and
S
k
is the socalled
Heisenberg
model
[
energy
]
∝
2
J
S
j
•
S
k
(Heisenberg)
(32.1)
where
•
J
> 0 makes the interaction attractive
•
the factor of 2 is chosen to ease the normalization later.
This form also appears for systems where the energy is proportional to the sum of spin
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 DavidBoal
 Physics, Energy, Statistical Mechanics, Fundamental physics concepts, Ising, Reif Ising

Click to edit the document details