Thermodynamics of lattice QCD with chiral 4-fermion interactions

We have studied lattice QCD with an additional, irrelevant 4-fermion interaction having a $\mathrm{U}\left(1\right)\mathrm{}\times \mathrm{U}\left(1\right)\mathrm{}$ chiral symmetry, at finite temperatures. Adding this 4-fermion term allowed us to work at zero quark mass, which would have otherwise been impossible. The theory with 2 massless staggered quark flavors appears to have a first order finite temperature phase transition at $N_t=4\mathrm{}$ for the value of 4-fermion coupling we have chosen, in contrast to what is expected for 2-flavor QCD. The pion screening mass is seen to vanish below this transition, only to become massive and degenerate with the σ ${(f}_0)$ above this transition where the chiral symmetry is restored, as is seen by the vanishing of the chiral condensate.