ABSTRACT
Among the many applications of statistical mechanics, some of the most intriguing and challenging theoretical problems arise in connection with phase transitions. These are abrupt changes of state such as occur, for example, when a liquid is transformed into a vapour, a ferromagnet loses its magnetization upon heating to its Curie temperature, or at the onset at suciently low temperatures of super uidity or superconductivity. It is within the theory of phase transitions, too, that the mathematical relationships between statistical mechanics and relativistic eld theories are most powerful. Indeed, the idea of spontaneous symmetry breaking, which lies at the heart of the theory of phase transitions, is the crucial ingredient that turns the gauge theories of Chapter 8 into a real working model of the fundamental forces of nature, to be discussed in the next chapter.
