HW3 - Physics 127B Homework Set 3(due February 3 Problem 1...

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Physics 127B – Homework Set 3: (due February 3) Problem 1, 2: Magnetic thin films Problem 1.6 in Kardar, “Statistical Physics of Fields,”, p. 17. This problem counts for two. You will learn a lot from it: Mean field for O(3) spins. How to set up mean field in an inhomogeneous system (here, due to boundaries, but also more generally) and calculate the correlation length (“healing length”). This provides great prequel to the Landau-Ginzburg theory in Chapter 2; I encourage you to read this chapter with this concrete example in mind. Finite size effects near criticality. “Surface layer”criticality. Some suggestions as you work through the problem From the start, orient all “trial fields” in the ˆ z spin direction and imagine even more general site-dependent trial fields h r (here site r = { i, α } , with α =layer label and i =site label in the layer); in the end, you will take h r to depend on the layer α only. In part d), minimize the trial free energy F trial = ( H ) 0 + F 0 − ( H 0 ) 0 with respect to each h
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