Thermal/Statistical Physics Paramagnet

1. Jan 31, 2006

NIQ

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
$$T = \frac{\tau}{k_B}$$
$$\frac{1}{\tau} = (\frac{\partial \sigma}{\partial U})_{N,V}$$
$$\therefore T(N,U,B) = \frac{2mB}{k_B} [ln(\frac{N}{2} - \frac{U}{2mB}) - ln(\frac{N}{2} + \frac{U}{2mB})]^{-1}$$

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:
$$M = -\frac{U}{B} = 2ms$$

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. Jan 31, 2006

Gokul43201

Staff Emeritus
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
3. Jan 31, 2006

NIQ

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

And my course is being taught by Erich Poppitz.

4. Feb 9, 2006

beee

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.