Many years ago I came across Salmhofer's Renormalization book and I studied its first chapter for a while. At the time, a professor told me the aim of the book was to develop a perturbative fermionic field theory at positive temperature and (I don't remember exactly why) I decided I should focus on something else and quit the book. It's not like I completely forgot of this book until now, but I was recently doing a little search on RG books, specially those intended to apply these techniques to statistical mechanics. I understand RG is not a theory per se, in the sense that it has many ways to be implemented, so I was searching those books which covered more or less the topics I'd like to learn. This beautiful answer helped me a lot, and again Salmhofer's showed to be a great book. My point here is what follows. I know that the aim of the book is to study fermionic field theories, as I pointed out, and this is specially done in chapter 4. However, the first three chapters seem to me a great general exposition, which are not only applicable to fermionic systems but, rather, to a vast range of systems in statistical mechanics. For instance, the book discusses topics such as Gaussian integrals, polymer expansions, Feynman graphs and so on. My question is whether I'm misunderstanding something or these techniques are really meant to be much more general indeed. In other words, is anything deeply hidden behind the techniques developed in the first three chapters of the book so that it does not apply to non-fermionic systems (or need to be adapted) or am I reading it correctly and these techniques are worth understanding even if I'm not interested in fermionic systems?
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$\begingroup$ For a fermionic system you would do Gaussian integrals with Grassman variables, while in a more general context you would also study complex or real variables. So yes, it makes sense to take the more general perspective, before focusing on the fermionic case. $\endgroup$– Carlo BeenakkerCommented May 20, 2020 at 9:48
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$\begingroup$ which "beautiful answer" is that? you linked to the question not a particular answer. $\endgroup$– Abdelmalek AbdesselamCommented May 20, 2020 at 14:01
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$\begingroup$ @AbdelmalekAbdesselam Ops! It's your answer. Well, all the other answers are useful too but your answer was really detailed and enlightening. $\endgroup$– JustWannaKnowCommented May 20, 2020 at 14:18
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$\begingroup$ @CarloBeenakker but that is the point. The book has an appendix on Grassmann variables and its associated calculus, but the exposure in the first few chapters states the results in real/complex variables. It really seems like a general approach since the discussion considers spin systems. $\endgroup$– JustWannaKnowCommented May 20, 2020 at 14:24
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1$\begingroup$ right, and since the difference real/complex/grassman is really not essential, you want to first introduce the topic with real or complex numbers, before adding the complexity of grassman calculus; the techniques are basically the same. $\endgroup$– Carlo BeenakkerCommented May 20, 2020 at 14:27
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