1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Thermal/Statistical Physics Paramagnet

  1. Jan 31, 2006 #1


    User Avatar

    Problem Set:

    http://www.physics.utoronto.ca/%7Epoppitz/hw2.pdf [Broken]

    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 by a moderator: May 2, 2017
  2. jcsd
  3. Jan 31, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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


    User Avatar

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook