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HW2 - Physics 127B Homework Set 2(due January 27 Problem 1...

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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 Ising-type? 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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