hw06soln

# hw06soln - 1 Homework 6(due November 24 Problem 6-1(5 pts...

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1 Homework 6 (due November 24) Problem 6-1 (5 pts.) Consider an antiferromagnetic Ising system on a cubic lattice: H = J 2 z X i,j nearest. neib σ i σ j B X i σ i Here J> 0 , z =6 is the number of nearest neibores per site. a) The lattice can be split onto two sublattices which tend to have opposite spins. Construct the mean f eld free energy of the system, as a function of two parameters, σ α and σ β de f ned as average spins of the two sublattices. b) By expanding the free energy in terms of σ α and σ β , up to 4-th order term, f nd the behavior of the order parameter ¡ σ α σ β ¢ / 2 , close to critical point, at zero f eld. Hint: it is useful to change the variables to σ = ¡ σ α σ β ¢ / 2 and σ + = ¡ σ α + σ β ¢ / 2 . c) Within the above Landau-type expansion, f nd the linear magnetic susceptibility of the system, above and below the antiferromagnetic transition. Demonstrate that within the mean f eld theory the derivative ∂χ/∂T experiences a jump at the critical point. Solution:

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hw06soln - 1 Homework 6(due November 24 Problem 6-1(5 pts...

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