Applications of quantum field theory to statistical mechanics

Abstract

Several concepts of quantum field theory in which Symanzik's work has been essential, have played a central role in statistical mechanics as well. The existence of a scaling limit near a critical point is a direct consequence of renormalization theory; scaling laws, indices and universality follow (as shown by Wilson) from the renormalization group framework, in field theory from the Callan-Symanzik equations; Symanzik's work on exceptional momenta, on the renormalization of broken symmetries, and on repeated insertions of mass operators gives important informations on the theory, for instance the possibility of calculating all the exponents at the critical temperature. Several other contributions of Symanzik, from the 1 N expansion to the Casimir effect and its relation to surface phenomena, are briefly reviewed.