ABSTRACT
Spontaneous symmetry breaking is ubiquitous, and is accompanied by important phenomena: the acquisition of rigidity, the existence of low energy excitations, and the possibility of topological defects. The physics is relevant to physical systems such as magnets, superfluids, superconductors, Heisenberg spin glasses, liquid crystals, rubber, not to mention the phase transitions which may have occured during the early universe. The chapter examines the response function for a system with O(n) symmetry. One important consequence of spontaneous symmetry breaking in systems with a continuous symmetry is the emergence of rigidity. This is intimately connected with the presence of power law correlations in the transverse response function. The chapter addresses the issue of the lower critical dimension for systems with a continuous symmetry. It discusses the stability of the ordered state by looking at the most dangerous modes, namely the transverse fluctuations.
