1999/09/08 by Alan Chodos, Fred Cooper, Wenjin Mao +2 · 7 citations
Physics and Astronomy · #High-Energy Particle Collisions Research #Pulsars and Gravitational Waves Research #Quantum Chromodynamics and Particle Interactions #astro-ph #hep-ph #hep-th #nucl-th
paper · pdf · doi:10.1103/physrevd.61.045011
published as Phys.Rev. D61 (2000) 045011 · 27 Pages, 7 embedded .eps figures, uses epsf
arxiv created 1999/09/08 · openalex publication_date 2000/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking (〈\ensuremathψ\ensuremathψ〉 condensate) and superconducting (Cooper pair 〈\ensuremathψ\ensuremathψ〉 condensates) phases at large N. At zero temperature and density, the model can be solved analytically in the large-N limit. We perform the renormalization explicitly and obtain a closed form expression of the effective potential. There exists a renormalization group invariant parameter \ensuremathδ that determines which of the 〈\ensuremathψ\ensuremathψ〉(\ensuremathδ>0) or 〈\ensuremathψ\ensuremathψ〉(\ensuremathδ<0) condensates exist in the vacuum. At finite temperatures and densities, we map out the phase structure of the model by a detailed numerical analysis of the renormalized effective potential. For \ensuremathδ positive and sufficiently large, the phase diagram in the \ensuremathμ\ensuremath-T (chemical potential-temperature) plane exactly mimics the features expected for QCD with two light flavors of quarks. At low temperatures there exists low-\ensuremathμ chiral symmetry breaking and high-\ensuremathμ Cooper pair condensate regions which are separated by a first-order phase transition. At high \ensuremathμ, when the temperature is raised, the system undergoes a second-order phase transition from the superconducting phase to an unbroken phase in which both condensates vanish. For a range of values of \ensuremathδ the theory possesses a tricritical point (\ensuremathμtc and Ttc); for \ensuremathμ>\ensuremathμtc(\ensuremathμ<\ensuremathμtc) the phase transition from the low temperature chiral symmetry breaking phase to unbroken phase is first order (second order). For the range of \ensuremathδ in which the system mimics QCD, we expect the model to be useful for the investigation of dynamical aspects of nonequilibrium phase transitions, and to provide information relevant to the study of relativistic heavy ion collisions and the dense interiors of neutron stars.