MIT OpenCourseWare http ocw mit edu 8 512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 1 8 512 Theory of Solids Problem Set 8 Due April 22 2004 1 a Using linear response theory derive the following expression for the magnetic susceptibility Mz Hz kT 1 e d Sz q Sz q q 0 2 b Provided that the total magnetization Mz i Siz commutes with the Hamil lim tonian we can start from the expression F kT ln T r e H Mz Hz and take derivatives with respect to Hz to derive the simpler expression 1 Mz2 kT Show that this is consistent with the more general expression obtained in 1 a Hint in this special case limq 0 Sz q 2 2 Using the results of Problem 1 a Calculate the low temperature T for a Heisenberg antiferromagnet Show that it is proportional to T 2 b For an antiferromagnet with an Ising anisotropy argue that e T What is the value of
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