Infrared problems and phase transitions of continuous order in low-dimensional systems
The infrared problem is the strong response, in particular logarithmic divergencies in perturbation theoretical treatments, of a system to perturbations which couple to low-lying energy excitations. Because of connections between phase space and momentum dispersion such problems arise normally in 1 and 2 space dimensions. In a unified description we show the mathematical equivalence of infrared behaviour for the following model situations: 1) 1-d Fermi systems with general interactions, 2) 1-d Bose systems with “Sine-Gordon” interaction, 3) the 2-d magnetic (harmonic) rotator model, 4) the 2-d classical Coulomb plasma.
Infrared singular behaviour is characterized by power law singularities in thermodynamic quantities with singular (or critical) exponents which usually vary continuously with system parameters. Depending or. the physical interpretation of these parameters in the different situations, this implies: 1) and 2): singular ground-state properties, a special particle spectrum and instabilities for correlation functions; 3): the phase transition of continuous order for 2-d magnetic systems and other systems with continuous symmetry; 4) a smooth metal-insulator transition and special thermodynamic properties in the Coulomb plasma.
KeywordsFermi System Rotator Model Infrared Behaviour Continuous Order Bose System
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