title: Infrared behavior in systems with a broken continuous symmetry: classical O(N) model versus interacting bosons.
abstract: In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued by infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result, the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O (N) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov's theory), large-N limit, and nonperturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale p{G}, below which the perturbative approach breaks down. Even though the action of (nonrelativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O(N) model and interacting bosons at zero temperature.
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, CNRS-UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris Cedex 05, France.
authors.forename: N
authors.initials: N
authors.lastname: Dupuis
mesh_terms: D000465:Algorithms; D057446:Hydrodynamics; D007259:Infrared Rays; D015233:Models, Statistical; D016011:Normal Distribution; D010825:Physics / Q000379:methods*; D013055:Spectrophotometry, Infrared; D013696:Temperature