Phase Structure of Lattice QCD at Finite Density with Dynamical Fermions

We compare the chemical potential associated with the onset of non-zero baryon number density on $6^4$ and $8^4$ lattices at $\beta=5.1$ and ma=0.01. We provide evidence for $Z(3)$ tunnelling. We determine a critical chemical potential of $\mu a \simeq 0.1$ which is unexpectedly low. We also determine the dependence of the onset of the observed phase transition on the quark mass. The physically misleading result of the quenched theory is shown to persist despite the inclusion of the complex fermion determinant.Comment: 3 pages, Latex, 5 postscript figures, Talk presented at LATTICE96(finite temperature

Lattice Gauge Theory Simulations at Nonzero Chemical Potential in the Chiral Limit

We present a method of simulating lattice QCD at nonzero chemical potential in the chiral limit. By adding a weak four-fermi interaction to the standard staggered fermion SU(3) QCD action, we produce an algorithm in which the limit of massless fermions is well-behaved and physical. Using configurations at zero chemical potential, and an exact fugacity expansion of the fermion determinant, we can simulate QCD at nonzero chemical potential and evade the notorious problem of the complex action. Small lattice simulations give physical results: At strong gauge coupling the critical chemical potential \mu_c agrees with theoretical expectations and at weak gauge coupling \mu_c is nonzero in the low temperature confined phase of QCD and jumps to zero in the high temperature quark-gluon plasma phase. In all these simulations the quarks are exactly massless and there is a Goldstone pion.Comment: contains .tex file of text and three figures as .epsi file

Analysis of the Lee-Yang zeros in a dynamical mass generation model in three dimensions

We investigate a strongly U(1) gauge theory with fermions and scalars on a three dimensional lattice and analyze whether the cintinuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the weak coupling region where a possible new dynamical mass generation mechanism might exist. There we investigate the mass of the composite fermion, the chiral condensate and the scaling of the Lee-Yang zeros.Comment: 3 pages,4 figures,talk presented at Lattice97(Edinburgh

Finite Density Fat QCD

Lattice formulation of Finite Baryon Density QCD is problematic from computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For large bare quark masses, instead, it is possible to obtain more sensible results; problems are still present but restricted to a small region. We present evidence for a saturation transition independent from the gauge coupling $\beta$ and for a transition line that, starting from the temperature critical point at $\mu=0$, moves towards smaller $\beta$ with increasing $\mu$ as expected from simplified phenomenological arguments.Comment: 14 pages, 10 figure

Finite Density QCD: a New Approach

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, test it in the Gross-Neveu model at finite baryon density, and apply it to the study of the chemical potential-temperature phase diagram of QCD with four degenerate flavors of Kogut-Susskind type.Comment: 21 pages, 9 figures. Some comments and references adde

Real and imaginary chemical potential in 2-color QCD

In this paper we study the finite temperature SU(2) gauge theory with staggered fermions for non-zero imaginary and real chemical potential. The method of analytical continuation of Monte Carlo results from imaginary to real chemical potential is tested by comparison with simulations performed {\em directly} for real chemical potential. We discuss the applicability of the method in the different regions of the phase diagram in the temperature -- imaginary chemical potential plane.Comment: 15 pages, 7 figures; a few comments added; version published on Phys. Rev.

Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density

We comment on the reweighting method for the study of finite density lattice QCD. We discuss the applicable parameter range of the reweighting method for models which have more than one simulation parameter. The applicability range is determined by the fluctuations of the modification factor of the Boltzmann weight. In some models having a first order phase transition, the fluctuations are minimized along the phase transition line if we assume that the pressure in the hot and the cold phase is balanced at the first order phase transition point. This suggests that the reweighting method with two parameters is applicable in a wide range for the purpose of tracing out the phase transition line in the parameter space. To confirm the usefulness of the reweighting method for 2 flavor QCD, the fluctuations of the reweighting factor are measured by numerical simulations for the cases of reweighting in the quark mass and chemical potential directions. The relation with the phase transition line is discussed. Moreover, the sign problem caused by the complex phase fluctuations is studied.Comment: 20 page, 6 figure

Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions

Complete spectra of the staggered Dirac operator \Dirac are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An attempt is made to relate the performance of multigrid (MG) and conjugate gradient (CG) algorithms for propagators with the distribution of the eigenvalues of~\Dirac. The convergence of the CG algorithm is determined only by the condition number~$\kappa$ and by the lattice size. Since~$\kappa$'s do not vary significantly when quarks become dynamic, CG convergence in unquenched fields can be predicted from quenched simulations. On the other hand, MG convergence is not affected by~$\kappa$ but depends on the spectrum in a more subtle way.Comment: 19 pages, 8 figures, HUB-IEP-94/12 and KL-TH 19/94; comes as a uuencoded tar-compressed .ps-fil

The QCD thermal phase transition in the presence of a small chemical potential

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $\mu$. Derivatives of the phase transition point with respect to $\mu$ are computed at $\mu=0$ for 2 flavors of p-4 improved staggered fermions with $ma=0.1,0.2$ on a $16^3\times4$ lattice. The resulting Taylor expansion is well behaved for the small values of $\mu_{\rm q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve $T_c(\mu)$ in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of $\mu\not=0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $\mu\not=0$.Comment: 26 pages, 25 figures, minor modificatio

Positivity of High Density Effective Theory

We show that the effective field theory of low energy modes in dense QCD has positive Euclidean path integral measure. The complexity of the measure of QCD at finite chemical potential can be ascribed to modes which are irrelevant to the dynamics at sufficiently high density. Rigorous inequalities follow at asymptotic density. Lattice simulation of dense QCD should be possible using the quark determinant calculated in the effective theory.Comment: 10 pages, Revised version, to appear in Rapid Communications of Physical Review