1. For a history of the Ising model seeS. G. Brush:Rev. Mod. Phys.,39, 883 (1969).
2. R. Peierls:Proc. Cambridge Phil. Soc.,32, 477 (1936).
3. L. Onsager:Phys. Rev.,65, 117 (1944).
4. T. D. Lee andC. N. Yang:Phys. Rev.,87, 410 (1952).
5. The mean field theory, as it appears from the literature quoted below, is a theory of phase transitions due to very-long-range and weak forces. The Ising model is, in contrast, a theory based on strong and short-ranged forces. The original approach to the Van der Waals theory (also called the mean field theory) can be found in the book byS. Chapman andT. Cowling:The Mathematical Theory of Nonuniform Gases (Cambridge, 1953), p. 284. A more refined and interesting formulation is inN. G. Van Kampen:Phys. Rev.,135, A 362 (1964). A rigorous and very clear theory is inJ. L. Lebowitz andO. Penrose:Journ. Math. Phys.,7, 98 (1966). The first to understand how to rigorously formulate (and prove in particular cases) the mean field theory have beenP. Hemmer, M. Kac andG. E. Uhlenbeck in a series of papers appeared inJourn. Math. Phys. and reproduced, with introductory remarks, inE. Lieb andD. C. Mattis:Mathematical Physics in One Dimension (New York, 1966). A more phenomenological but very interesting and original theory is in the book ofR. H. Brout:Phase Transitions (New York, 1965), where the most common phase transitions are treated from the unifying point of view of the mean field theory.