What is a good textbook on statistical field theory, with an emphasis on applications to non-equilibrium phenomena?
I am a final-year undergraduate, have already taken introductory classes in statistical physics and quantum mechanics but do not know a lot of quantum field theory yet. I would like to better understand nonequilibrium phenomena, phase transitions and spontaneous symmetry breaking in condensed matter systems.
Answer
A classic on the subject is Giorgio Parisi's Statistical Field Theory. It is a complete book written by one of the most influential physicists in the field.
The book starts with a brief recap on statistical mechanics and then introduces the Ising Model, were the basic techniques of statistical field theory are introduced. It then moves on to (in this order): Landau-Ginzburg model, renormalization group, spontaneous symmetry breaking, path integrals and relativistic QFT. At the end of the book you will also find two brief sections on stochastic methods and computer simulations.
The style is clear but really dense, and sometimes you will discover that you will need three pages to prove a formula that is considered almost trivial by the author, but the satisfaction you get is worth the effort and you will often find really deep insights. Anyway if you have a solid background in statistical mechanics, quantum mechanics and mathematics you shouldn't have any problem.
If you want to understand nonequilibrium phenomena, phase transitions and spontaneous symmetry breaking you could also try Kerson Huang's Statistical Mechanics. Although it is not really a SFT book, it covers in a really clear, concise manner Ising Model, critical phenomena, Landau-Ginzburg and renormalization group.
There is also a chapter about the partition function which I found really helpful to understand how complex singularities in the partition function can lead to phase transitions.
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