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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!

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# Homework Help: Thermal/Statistical Physics Paramagnet

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