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

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Unformatted text preview: 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 layercriticality. Some suggestions as you work through the problem From the start, orient all trial fields in the z spin direction and imagine even more general site-dependent trial fields h r (here site r = { i, } , with =layer label and i =site label in the layer); in the end, you will take h r to depend on the layer only. In part d), minimize the trial free energy...
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HW3 - Physics 127B Homework Set 3: (due February 3) Problem...

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