1. A few well-known basic results -- 2. Introduction: order parameters, broken symmetries -- 3. Examples of physical situations modelled by the Ising model -- 4. A few results about the Ising model -- 5. High temperature and low temperature expansions -- 6. Some geometric problems related to phase transitions -- 7. Phenomenological description of the critical behaviour -- 8. Mean field theory -- 9. Beyond mean field theory -- 10. Introduction to the renormalization group -- 11. Renormalization group for the [phi]4 theory -- 12. Renormalized theory -- 13. Goldstone modes -- 14. Large n.
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"Knowledge of the renormalization group and field theory is a key part of physics, and is essential in condensed matter and particle physics. Written for advanced undergraduate and beginning graduate students, this textbook provides a concise introduction to this subject. The textbook deals directly with the loop-expansion of the free-energy, also known as the background field method. This is a powerful method, especially when dealing with symmetries, and statistical mechanics. In focussing on free-energy, the author avoids long developments on field theory techniques. The necessity of renormalization then follows"--