Lecture 24 - Magnetic Phase Transition in the...

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Magnetic Phase Transition in the Infinite-range model and its connection to the Mean-Field Model 1 ij i j N J N      H 1 N term necessary for thermodynamic limit to exist Note:       2 22 1 2 1 2 1 2 2 222 1 2 2 3 1 3 1 2 3 1 2 3 2 2 . etc   Hence, 2 2 11 2 2 1 {} but 1, so NN ii i N i i JJ N          i i N Qe  define JK   2 2 2 i i K K N ee Use the identity 2 2 2 2 1 2 x a ax e e dx   This is just a Gaussian integral but in this context it is called the Hubbard-Stratanovich Transformation 1/2 Choose i K a N 2 2 1 exp 2 2 i K Ni xK Q e x dx N      Spins are now decoupled and we know that 1 i 
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2 2 1 exp 2cosh 2 2 N K N xK
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This note was uploaded on 09/28/2011 for the course PHYSICS 971 taught by Professor Chakabarti during the Spring '10 term at Kansas State University.

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Lecture 24 - Magnetic Phase Transition in the...

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