Phase transition in the massive Gross-Neveu model in toroidal topologies

Abstract

We use methods of quantum field theory in toroidal topologies to study the N-component D-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-N coupling constant (g), investigating its dependence on the compactification length (L) and the temperature (T). For all values of the fixed coupling constant (λ), we find an asymptotic-freedom type of behavior, with g→0 as L→0 and/or T→∞. At T=0, and for λ≥λ(D)c (the strong-coupling regime), we show that, starting in the region of asymptotic freedom and increasing L, a divergence of g appears at a finite value of L, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, L(D)c, and the deconfining temperature, T(D)d, are determined as functions of λ and the mass (m) of the fermions, in the case of D=2,3,4. Taking m as the constituent quark mass (≈350 MeV), the results obtained are of the same order of magnitude as the diameter (≈1.7 fm) and the estimated deconfining temperature (≈200 MeV) of hadrons.