p847ps5 - have a “staggered magnetic feld” which equals...

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Physics 847: Problem Set 5 Due Thursday, May 13 at 11:59 P. M. Each problem is worth 10 points unless otherwise specifed. 1. Consider a Ferromagnetic Ising model with nearest neighbor interac- tions on a simple cubic lattice. Each spin thus has 6 nearest neighbors. IF there are a total oF N spins on the lattice, calculatethe energy and degeneracy oF the frst excited state. 2. Pathria, Problem 11.9. Skip the Heisenberg interaction in this prob- lem. “High temperatures” means temperatures greater than the Neel (antiFerromagnetic ordering) temperature. 3. Consider the model oF problem 11.9 (the antiFerromagnetic Ising model), but instead oF a uniForm applied magnetic feld B, assume that you
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Unformatted text preview: have a “staggered magnetic feld” which equals B on one sublattice and -B on the other. Defne a “staggered susceptibility” which equals ( ∂M/∂B ) B =0 , where M is the magnetization on one oF the sublattices. Show that in the mean feld approximation, this staggered susceptibil-ity diverges as T approaches the Neel temperature T N From above, with temperature dependence 1 / ( T-T N ). 4. Pathria, Problem (11.12) (20 pts.). Skip the sentence beginning “±ur-ther show that. ..” Also, fnd the critical temperature at x = 1/2 in terms oF the interaction parameters ǫ . 1...
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