I am Studying Phase Transitions, starting from simple VdW equation up to Mean-Field&Landau Theory. I have many books such as Huang Kerson-Statistical mechanics, Yeomans- Statistical Mechanics of phase Transitions, Lubensky, Kardar and they've covered me so far for MFT.

However I have trouble finding a bit more advanced cases of MFT in these books, including:

i) Detailed analysis on Landau–Ginzburg Theory

Books/notes usually only cover the simplest case $f=f_0 +am^2+bm^4 +k(\nabla m )^2 $, what do we do when there are terms of higher order ( such as $ (\nabla^2 m )^2$) and what's the physical difference?

ii) Ornstein–Zernike approximation

I've come across this when solving a system with the above free energy and reading about the corelation function, but have yet to see a book that gives me a detailed explanation of what it is, how it works and why we do it.

iii) Cahn – Hilliard theory

None of the above books covers this

iv) Nematic to Smectic Transition

v) Spinodal decomposition


Huang's book covers this. However the exact mathematical formalism and arguments in Haung are not very clear to me. I would like a book that treats the Renormalization Group in an abstract rigorous manner so that I can understand the key concepts.

In general I have so far studied from all these books collectively, switching from one to the other, including some lecture notes I've found.

I would like book/lecture notes recommendations (undergrad or probably graduate level) that go into detail in these advanced (?) cases of phase transitions and meant for someone that is reading these for the first time, but has of course a backround in statistical physics, if such books exist.


2 Answers 2


I'm not sure everything you ask is in it, but I really like Lectures On Phase Transitions And The Renormalization Group (Frontiers in Physics) by N. Goldenfeld which treats in detail the Renormalization group approach to phase transition. It's not the most mathematical book on the subject, but there is a pretty good physical intuition and largely enough algebra to get you going. I strongly recommand it reading for whoever want to study phase transition


The statistical physics book by Linda Reichl is easy to read and has some of the advanced material. A good complement for the renormalization aspect are Goldenfeld's Lectures On Phase Transitions And The Renormalization Group.


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