Spatial confinement and thermal deconfinement in the 3D Gross-Neveu model

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. From the four-point function, we obtain a closed expression for the large-N effective coupling constant g=g(L,T,λ). Different behavior depending on the magnitude of the fixed coupling constant λ is found to lead to a “critical” value λc. If λ<λc, only short-distance and/or high-temperature “asymptotic freedom” (g→0) is found. For λ⩾λc, and low enough T, one also observes a divergence in g as L→Lc, suggesting that fermions become spatially confined, an effect which is destroyed by raising the temperature. We find a confining length, Lc≃1.61fm, that is close to the proton charge diameter (≈1.74fm) and a “deconfining” temperature, ≃138MeV, which is comparable to the estimated value of the deconfining temperature (≈200MeV) for hadrons.