- #1

- 19

- 0

I have just started reading up on mean field theory. Any book you could refer??

You should upgrade or use an alternative browser.

- Thread starter sridhar
- Start date

- #1

- 19

- 0

I have just started reading up on mean field theory. Any book you could refer??

- #2

Chris Hillman

Science Advisor

- 2,345

- 8

- #3

- 19

- 0

"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.

- #4

Chris Hillman

Science Advisor

- 2,345

- 8

For example, if you don't know about coupling from the past you are killing yourself by limiting yourself to mean-field theory!

- #5

- 19

- 0

- #6

Chris Hillman

Science Advisor

- 2,345

- 8

Seriously, if you don't know about coupling from the past you won't regret learning about it.

- #7

- 19

- 0

I am sure I can find it in a library. I would really appreciate some help with my mean field theory issue. I cant find a book which describes various lattice models and their mean field treatments.

- #8

Chris Hillman

Science Advisor

- 2,345

- 8

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.)

Last edited:

Share: