This book is devoted to a thorough analysis of the role that models play in the practise of physical theory. The authors, a mathematical physicist and a philosopher of science, appeal to the logicians’ notion of model theory as well as to the concepts of physicists.

Two alternative accounts of quantum spontaneous symmetry breaking (SSB) are compared and one of them, the decompositional account in the algebraic approach, is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account -- the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.