I welcome comments and suggestions. However, bear in mind that my target audience is not the typical reader of this blog, but rather your non-physicist friends and family.
I think it still needs a lot of work, particularly to be less technical. I still have not figured out how to explain how fluctuations are larger in lower dimensions.
The goal is for it to be interesting, accessible, and bring out the excitement and importance of condensed matter physics.
I found a simple explanation in the book "Principles of Condensed Matter Physics" by Chaikin and Lubensky. Quote from p. 15 "8 Fluctuations and spatial dimension":
ReplyDelete"This is essentially a problem of connectivity. The only way one end of a one-dimensional system knows what is going on at the other end is via information transmitted directly along the chain. For an infinitely long system, any fluctuation cuts the flow of information and hence the order. Since there are always fluctuations at any finite temperature, a one-dimensional system cannot be ordered except at zero temperature. In two-dimensional systems, there are many paths that can connect one part of the system to the others."
Thanks that is very helpful.
DeleteI read this Flatland book in my 1st year of PhD. Honestly, that was the hardest book I read. Not because the content is difficult to understand, but because of its view of women. I'm glad the referral to women vs men made in Flatland is not in your draft :)
ReplyDeleteHanna, Thanks for the comment. I wasn't sure whether to mention that. In the second edition preface the author claimed that he was providing a satire of the views of this time not endorsing them.
Deletehttps://en.wikipedia.org/wiki/Flatland#As_a_social_satire
I am glad things have changed; albeit, not as much as they should.
Hi Ross,
ReplyDeleteHow fluctuations are larger in lower dimensions: isn't it for the same reason as to why the mean-field theories/order are better in higher dimensions. I am sure you have already covered and explained this in another chapter (haven't you?), so I am curious to know what is it that you are concerned about.