P28 of phase transitions and the renormalization group

In summary, the conversation discusses confusion about a specific topic in Nigel Goldenfeld's book, "Lectures on phase transitions and the renormalization group." The topic involves computing the potential energy of a uniformly charged sphere with a non-Gauss's law interaction potential. After a change of variables, it is believed that the author neglects to restrict the range of one variable, resulting in a disagreement with the final computation. This potential mistake is not mentioned in the book's errata.
  • #1
A_B
93
1
Hi,

I'm confused about the discussion on p28 of Nigel Goldenfeld's "Lectures on phase transitions and the renormalization group" (this question can only be answered by people who have access to the book.)

The goal is to compute the potential energy of a uniformly charged sphere where the interaction potential goes as [itex] 1/r^\sigma [/itex] (So Gauss's law isn't valid). I think that, after the change of variables (x,y) -> (u, v) he neglects to restrict the range of u to the intersection of two unit spheres that are translated a distance v with respect to each other. The final result of the computation also does not agree with the case [itex] \sigma=2 [/itex].

This is however not mentioned the errata (http://guava.physics.uiuc.edu/~nigel/errata.html) so maybe I'm missing something.Thanks,

A_B
 
  • #3
Seconded. I think it is a mistake.
 

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