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Reference request for path integral representation of 2D Ising model

Physics Asked on May 13, 2021

I’m looking for references that discuss the path integral approach for the two-dimensional Ising model, constructed from its transfer matrix. The only reference I know on the topic is this book, but their exposition is not much clear to me, since some details seem to be missing. Any help is appreciated.

One Answer

One textbook option is Quantum Field Theory and Condensed Matter by Shankar, which treats both the classical-quantum mapping and the two dimensional Ising model quite carefully. Another textbook-like option is McGreevy's Where do quantum field theories come from? lecture notes, which includes this topic as one example of the classical-quantum mapping. It's also worth checking out the paper Order and disorder in gauge systems and magnets by Fradkin and Susskind, which treats this mapping rather early on. Finally, John Kogut's classic review An introduction to lattice gauge theory and spin systems is a great reference for this topic, and treats the 2d Ising model fairly early on. Note that all of these references essentially cannibalize off each other (technically, from a historical perspective, Kogut's review encompasses Fradkin/Susskind's work, and Shankar/McGreevy were likely working closely along the lines of Kogut's review article), so any of these would be a good choice as a starting point.

Answered by Zack on May 13, 2021

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