lec35 - MIT OpenCourseWare http://ocw.mit.edu 8.044...

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Unformatted text preview: 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 . Simple Quantum Paramagnet, Canonical Ensemble Origin of magnetic moments: Electron spin and orbital angular momentum S + h/ 2 m e c L J = g J B J B e Nuclear angular momentum h/ 2 m p c I = g I N I N e 8.044 L35B1 m = g B H m 2J + 1 m = J, J 1 , J g B H Z 1 ( T, H ) = J e m /kT = J ) m = sinh[( J + 1 2 ) ] sinh[ 1 2 ] ( e m = J m = J g B H = level spacing kT kT Note Z 1 = Z 1 ( ) Z = Z 1 ( ) N = Z ( ) at fixed N 8.044 L35B2 e m /kT /Z 1 = p ( m ) = e m /Z 1 < > = m ( g B m ) e m Z 1 = g B 1 Z 1 Z 1 g B JB J ( ) M = N < > = g B NJB J ( ) 1 B J ( ) = J 1 Z 1 Z 1 1 1 = 1 ( J + 1 ) coth[( J + ) ] coth[ 1 ] J 2 2 2 2 This is called the Brillouin Function....
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lec35 - MIT OpenCourseWare http://ocw.mit.edu 8.044...

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