Physics 127B – Homework Set 2:
(due January 27)
Problem 1: The binary alloy
Problem 5.10 in Kardar, p. 155.
After you do this problem, take a look at Mike Cross’ lecture 4 – you should now be able to follow
general discussion of phase transitions in mixtures.
Problem 2: Critical point behavior
Problem 5.9 in Kardar, p. 154.
If you need more guidance than provided in the problem, you can consult posted notes on the
critical point behavior in the Van der Waals gas (but remember that your equation of state is
different).
Problem 3: Classical ground states in spin models
a) Consider the Heisenberg spin model with
antiferromagnetic
interactions, i.e.,
H
=

J
summationdisplay
(
ij
)
S
i
·
S
j
(1)
with
J <
0 (
∑
(
ij
)
denotes summation over nearest neighbor links). What is the classical ground
state on the cubic lattice?
How is the answer different if the spins are XY or Isingtype?
How
many ground states are there in each case?
b) Consider the nearest neighbor Heisenberg antiferromagnet on the triangular lattice. Show that
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 Winter '11
 OlexeiMotrunich
 Physics, Magnetism, Work, Fundamental physics concepts, Ferromagnetism, ground states

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