11 Symmetry Breaking in the Ising Mode

Abstract

Most of the theoretical wisdom on the phase transition of the ferromagnetic type and the related symmetry breaking is based on the two-dimensional Ising model, which also played the role of a laboratory for ideas and strategies and it is now regarded as a corner stone in the foundations of statistical mechanics. Anyone interested in critical phenomena and in the functional integral approach to quantum field theory should have a look to the model. Even if a discussion of the two-dimensional Ising model would be very appropriate for our purposes, we refer the reader to the very good accounts which can be found in literature. We restrict our discussion to the one-dimensional version of the model, which is almost trivial, but nevertheless provides an interesting simple example for testing the constructive strategies of symmetry breaking discussed above.