Mean Field Theory: Get Book Recommendations

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Discussion Overview

The discussion revolves around seeking book recommendations for understanding mean field theory, with a focus on its application to various models beyond the Ising model. Participants express interest in resources that provide a comprehensive introduction to mean field theory and its treatments of different lattice models.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks book recommendations for mean field theory, specifically looking for texts that cover multiple models in detail.
  • Another participant suggests that the inquiry may be more about finding a good introduction to the Ising model rather than mean field theory in general.
  • A participant clarifies that they are interested in mean field theory as it applies to the Heisenberg and n-potts models, and its behavior in infinite dimensions.
  • There is mention of the technique "coupling from the past" as a valuable concept that could enhance understanding of mean field theory.
  • A recommendation is made for a textbook by Haggstrom that introduces coupling from the past and its applications in Monte Carlo methods, which may be relevant to the discussion of mean field theory.

Areas of Agreement / Disagreement

Participants express differing views on the focus of the inquiry, with some suggesting a need for resources specific to the Ising model while others emphasize a broader interest in mean field theory. The discussion remains unresolved regarding the best resources to recommend.

Contextual Notes

Participants have varying levels of familiarity with concepts such as coupling from the past and different lattice models, which may influence their recommendations and understanding of mean field theory.

Who May Find This Useful

Readers interested in statistical mechanics, particularly those looking to deepen their understanding of mean field theory and its applications to various models.

sridhar
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I have just started reading up on mean field theory. Any book you could refer??
 
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What books have you read so far? I can think of one book which I would recommend which would be confusing unless you have read more modern books.
 
I have done upto the mean field treatment for ising model from
"Introduction to stat mech" Chandler which is by no means exhaustive.
I have also read Kerson Huang but again only the Ising model is discussed briefly.
I need a book which deals with few more models in detail.
 
A-haaa! So you want the Ising model, not mean-field theory in general? Is it possible that your real question is: what is a good introduction to the theory of the Ising model?

For example, if you don't know about coupling from the past you are killing yourself by limiting yourself to mean-field theory!
 
nono. Not at all. A book which introduces mean field theory. Not at all specific to the Ising model. In fact, I need to see how mean field theory treats Heisenberg and n-potts state(I like calling it that!) models. How it becomes exact for infinite dimensions, etc
 
Hmm... not sure I can help you there. Is Kenneth Wilson in the house?

Seriously, if you don't know about coupling from the past you won't regret learning about it.
 
I would love to learn more. The only coupling I know of is nearest neighbour for Ising model. Basically haven't ventured beyon spin 1/2 systems!
I am sure I can find it in a library. I would really appreciate some help with my mean field theory issue. I can't find a book which describes various lattice models and their mean field treatments.
 
Coupling from the past allows one to obtain a sample from the exact critical distribution, say for the Ising model. The nice undergraduate textbook by Haggstrom, Finite Markov Chains and Algorithmic Applications, London Mathematical Society student texts Vol. 52, University of Cambridge Press, 2002, is basically an introduction to this powerful and amazing technique, which can be used to give reliable Monte Carlo estimates of quantities of interest. There are many eprints on the arXiv which have been inspired by the original paper by Wilson and Propp. (See Fig. 12 in this book for a simulation of the 2x2 Ising model on a 15 by 15 square. If that sounds unimpressive, remember that this simulation uses the exact stationary distribution, not an approximation to it, which basically avoids all the problems of mean-field or whatnot.)
 
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