We consider the N-components 3-dimensional massive Gross-Neveu model compactified in one spatial direction, the system being constrained to a slab of thickness L. We derive a closed formula for the renormalized L-dependent four-point function at vanishing external momenta in the large-N limit (the effective coupling constant), using bag-model boundary conditions. For values of the fixed coupling constant in absence of boundaries lambda greater than or equal to lambda(c) similar or equal to 19.16, we obtain small-distance asymptotic freedom (for L --> 0) and a singularity for a length L-(c) such that 2.07m(-1) < L-(c) less than or similar to 2.82m(-1), m being the fermionic mass. Taking for P which is comparable with m an average of the masses of the quarks composing the proton, we obtain a "confining" length L-p((c)) an estimated proton diameter. (C) 2004 Published by Elsevier B.V. References: 20
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