Chiral symmetry restoration in the three-dimensional four-fermion model at non-zero temperature and density

The three-dimensional four-fermion model with a Z_2 chiral symmetry and N=4 fermion species in the system is investigated numerically at non-zero temparature and chemical potential. The phase diagram in the (chemical potential, temperature) plane is mapped out quantitatively. A detailed finite size scaling analysis shows that the zero temperature and non-zero chemical potential chiral phase transition is first order, whereas the non-zero temperature and non-zero chemical potential transition remains second order down to very low temperatures. Quantitative results for the location of the end of the first order line are given. The simulations at T=0 provided no evidence for a nuclear liquid-gas transition.Comment: 23 pages, 15 figure

Phase diagram of the three-dimensional NJL model

With the exception of confinement the three-dimensional Nambu-Jona-Lasinio (NJL_3) model incorporates many of the essential properties of QCD. We discuss the critical properties of the model at nonzero temperature T and/or nonzero chemical potential $\mu$. We show that the universality class of the thermal transition is that of the d=2 classical spin model with the same symmetry. We provide evidence for the existence of a tricritical point in the ($\mu$,temperature) plane. We also discuss numerical results by Hands et al. which showed that the system is critical for $\mu>\mu_c$ and the diquark condensate is zero.Comment: 3 pages, To appear in the proceedings of Conference on Quarks and Nuclear Physics (QNP 2002), Julich, Germany, 9-14 Jun 200

Results on Finite Density QCD

A brief summary of the formulation of QCD at finite chemical potental, $\mu$, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential $\approx { {m_{\pi}} \over 2}$. However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, ($e^{\mu/T}$), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when $\mu$ passed through the value m_{\pi}/2}.Comment: 14 pages, Latex, 18 eps figures, Review for Tsukuba worksho

Non-Compact QED_3 with N_f=1 and N_f=4

We present numerical results for non-compact three-dimensional QED for numbers of flavors N_f=1 and N_f=4.In particular, we address the issue of whether chiral symmetry is spontaneously broken in the continuum limit, and obtain a positive answer for N_f=1, with a dimensionless condensate estimated to be beta^2 ~= O(10^-3), implying that the critical number of flavors N_fc>1. We also compare the N_f=1 and N_f=4 models by analysing the transition from strong to weak coupling behaviour using an equation of state based on a continuous phase transition. While some qualitative differences emerge, it appears difficult to determine whether N_f=4 lies above or below N_fc.Comment: 19 pages, 10 figure

Rigorous arguments against current wisdoms in finite density QCD

QCD at finite chemical potential is analytically investigated in the region of large bare fermion masses. We show that, contrary to the general wisdom, the phase of the fermion determinant is irrelevant at zero temperature. However if the system is put at finite temperature, the contribution of the phase is finite. We also discuss on the quenched approximation and suggest that the origin of the failure of this approximation in finite density QCD could relay on the fundamental role that Pauli exclusion principle plays in this case.Comment: 16 pages, 5 figure