Confinement in the 3-dimensional Gross-Neveu model at finite temperature

Abstract

We study the N-component (2+1)-dimensional Gross-Neveu model bounded between two parallel planes separated by a distance L at finite temperature (T). We obtain a closed expression for the large-N effective coupling constant g = g(L,T,l). Different behavior depending on the magnitude of the fixed coupling constant l is found to lead to a ''critical'' value lc. If l < lc, only short-distance and/or high-temperature asymptotic freedom is found. For l > lc one also observes spatial confinement, which is destroyed by temperature effects. We find a confining length, Lc ~ 1.61 fm, that is close to the proton charge diameter ( » 1.74 fm) and a deconfining temperature, ~ 138 MeV, which is comparable to the estimated value of » 200 MeV for hadrons.