Chiral symmetry restoration and realisation of the Goldstone mechanism in the U(1) Gross-Neveu model at non-zero chemical potential

We simulate the Gross-Neveu model in 2+1 dimensions at Iron-zero baryon den sity (chemical potential mu not equal 0). It is possible to formulate this model with a real action and therefore to perform standard hybrid Monte Car lo simulations with mu not equal 0 in the functional measure. We compare th e physical observables from these simulations with simulations using the Gl asgow method where the value of mu in the functional measure is fixed at a value mu(upd). We find that the observables are sensitive to the choice of mu(upd). We consider the implications of our findings for Glasgow method QC D simulations at mu not equal 0. We demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu model is fundamentally different fr om that in QCD. We find that this difference explains why there is an unphy sical transition in QCD simulations at mu not equal 0 associated with the p ion mass scale whereas the transition in the Gross-Neveu model occurs at a larger mass scale and is therefore consistent with theoretical predictions. We note classes of theories which are exceptions to the Vafa-Witten theore m which permits the possibility of formation of baryon number violating diq uark condensates. (C) 1999 Published by Elsevier Science B.V. All rights re served.