Lecture 22 - Now look at the eqn. of state (h 0) define Tc...

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Now look at the eqn. of state ( 0) h define / c TT         tanh tanh / tanh 1 tanh / tanh tanh( ) tanh 1 tanh( ) B B B B h mm kT h k T m h k T m h m m k T m m       (Note that is not small!) Then for small h and m we can expand the tanh -function as 3 tanh 3 x xx  .     3 3 3 1 3 B m h m     3 32 (1 ) 1 3 m m m          3 3 1 B h Equation of State 1) Set 0 h to study spontaneous magnetization   2 2 3 01 3 1 1 3 1 (note m    0) c T T 2 ) 3 1 3 3 3 (2) 1 1 1 1 3 define 1 c c c c c c c cc T T T T T T T T m T T T T T T t        
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  1 22 Then, 3 1 3 (1 ) 3 3 3 as 0 m t t t t t t t t Thus, we see that the order-parameter exponent is 1 2
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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 22 - Now look at the eqn. of state (h 0) define Tc...

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