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I'm looking for references covering the following topics: path integrals in statistical mechanics and Wick rotations, second quantization, fermionic systems and Ising-like models and mean field theory. I have a background in quantum mechanics, statistical mechanics and thermodynamics.

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3 Answers 3

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The book by Altland and Simons has rather a detailed and exhaustive introduction to the second quantization, path integral formalism for bosonic and fermionic fields, with some exercises to check the understanding of the topics.

These topics are also covered rather well in the book by Shankar. Here you can find a long discussion of Ising model, from different aspects and perspectives.

References:

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Second Quantization is very good thing to start with anything. After that you may want to see lecture notes of Feynman, which cover all topics you mentioned, but I will recommend that only if you have done first course Statistical Mechanics properly. It is good to start with some application parts, like BCS theory. This will give some flavor of Wick's rotation, second quantization, fermionic system. David Tong's lecture notes will also prove to be helpful.

For Ising-like models which exhibit quantum phase transition, you can refer to any Quantum Phase Transition book or you can develop better understanding for Ising model.

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I think to study second quantization from path integrals, use Gauge field theory by Stefan Pokorski as 1st choice and use Peskin and Schroeder as second choice.

References:

  • S. Pokorski, Gauge Field Theories, doi:10.1017/CBO9780511612343.
  • M. E. Peskin & D. V. Schroeder, An Introduction to Quantum Field Theory.
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