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.
 

1. What is the significance of P28 in phase transitions and the renormalization group?

P28 refers to the 28th page of a research paper or textbook that discusses the topic of phase transitions and the renormalization group. This page may contain important information, equations, or diagrams related to these concepts.

2. How do phase transitions occur?

Phase transitions occur when a physical system undergoes a sudden change in its properties, such as its temperature or pressure. This change can be triggered by external factors or internal interactions between particles.

3. What is the role of the renormalization group in studying phase transitions?

The renormalization group is a mathematical and analytical tool used to study the behavior of systems at different length scales. It allows scientists to understand how a physical system behaves on a macroscopic level based on the interactions between its microscopic components.

4. Can the renormalization group be applied to other fields besides phase transitions?

Yes, the renormalization group has been used in various fields of physics, including quantum field theory, statistical mechanics, and condensed matter physics. It has also been applied in other disciplines, such as economics and computer science.

5. How does the renormalization group help us understand the universality of phase transitions?

The concept of universality in phase transitions refers to the fact that different physical systems can exhibit similar behavior and critical points, despite having different microscopic details. The renormalization group provides a framework for understanding this universality by identifying common features and scaling laws in various systems.

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