lec34 - MIT OpenCourseWare http:/ocw.mit.edu 8.044...

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MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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± PARAMAGNETS Spin 1/2 Paramagnet, Microcanonical Ensemble Assume the moment is parallel to the spin. Take n to be the state variable. µ is the magnetic moment of the particle. n H = Hz ˆ µ H µ = µ ˆ ( ) ,N = N n, ± z, ² = µH N-n - µ H ( ) ,N = n, ± z, ² = µH µ = µ ˆ 8.044 L34B1
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M = µ ( N N )= µ ( N 2 n )= M ( n ) N ± + N ± = µH ( N 2 n )= HM ( n ) E N ± ± ² = ± ²³ ´ ↑ ↑ ↓ ↓ H & n N ! S = k ln = S ( n ) n !( N n )! k [ N ln N n ln n ( N n ) ln( N n )] 8.044 L34B2
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± ² ± ² ± ² ± ² dS n = k [ 1 ln n +1+ln( N n )] = k ln dn N n S = S ( n ) and M = M ( n ) S = S ( M ) 1 ± ∂S ² = does not exist! T ∂E M H ∂S dS ∂n n 1 = = = k ln N n 2 µ T ∂M E dn ∂M E 8.044 L34B3
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This note was uploaded on 11/08/2011 for the course PHYSICS 8.004 taught by Professor Staff during the Spring '08 term at MIT.

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lec34 - MIT OpenCourseWare http:/ocw.mit.edu 8.044...

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