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Thermal/Statistical Physics Paramagnet

  1. Jan 31, 2006 #1

    NIQ

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    Problem Set:

    http://www.physics.utoronto.ca/~poppitz/hw2.pdf

    I'm having a problem with I.3

    I got I.1 (answer is given on sheet)
    For I.2 I found T(N,U,B) the following way
    [tex]T = \frac{\tau}{k_B}[/tex]
    [tex]\frac{1}{\tau} = (\frac{\partial \sigma}{\partial U})_{N,V}[/tex]
    [tex]\therefore T(N,U,B) = \frac{2mB}{k_B} [ln(\frac{N}{2} - \frac{U}{2mB}) - ln(\frac{N}{2} + \frac{U}{2mB})]^{-1}[/tex]

    The problem I was having with I.3 is that I don't know how to go about finding the maximum magnetization. I remember hearing in class that the magnetization is maximized when the temperature is 0 but... it wouldn't make sense if B=0 and m can't be 0 so there's no other way of making that equation equal to 0.

    I know the following is true:
    [tex]M = -\frac{U}{B} = 2ms[/tex]

    But I'm not quite sure what I can do with this...

    Any help would be greatly appreciated, thanks!
     
    Last edited: Jan 31, 2006
  2. jcsd
  3. Jan 31, 2006 #2

    Gokul43201

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    Can you not simply rewrite T(N,U,B) as U(T,N,B) ?

    PS : Is this course being taught by Yong Baek Kim ?
     
    Last edited: Jan 31, 2006
  4. Jan 31, 2006 #3

    NIQ

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    Ok I'll try to do that and let you know.

    And my course is being taught by Erich Poppitz.
     
  5. Feb 9, 2006 #4
    I guess the only thing to do is take a limit of M(B, T, N) as T goes to zero. That seems to work perfectly and agrees with common sense in the end.
     
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