The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $\mu$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $\mu$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.Comment: 42 pages revtex, 25 figures postscrip

Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model

We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean dimensions. Different model equations of state, corresponding to different theoretical scenarios, are tested against the order parameter data. The results are sensitive to necessary assumptions about the shape and extent of the scaling region. Our best fits favour a trivial scenario in which the logarithmic corrections are qualitatively similar to those predicted by the large N_f approximation. This is supported by a separate analysis of finite volume corrections for data taken directly in the chiral limit.Comment: 37 pages LaTeX (RevTeX) including 12 .eps figure

Isospin Chemical Potential and the QCD Phase Diagram at Nonzero Temperature and Baryon Chemical Potential

We use the Nambu--Jona-Lasinio model to study the effects of the isospin chemical potential on the QCD phase diagram at nonzero temperature and baryon chemical potential. We find that the phase diagram is qualitatively altered by a small isospin chemical potential. There are two first order phase transitions that end in two critical endpoints, and there are two crossovers at low baryon chemical potential. These results have important consequences for systems where both baryon and isospin chemical potentials are nonzero, such as heavy ion collision experiments. Our results are in complete agreement with those recently obtained in a Random Matrix Model.Comment: 4 pages, 1 figure, REVTeX

Complex Langevin Simulations of QCD at Finite Density -- Progress Report

We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance sampling fail. Adaptive methods and gauge-cooling are used to prevent runaway solutions. Even then, the CLE is not guaranteed to give correct results. We are therefore performing extensive testing to determine under what, if any, conditions we can achieve reliable results. Our earlier simulations at $\beta=6/g^2=5.6$, $m=0.025$ on a $12^4$ lattice reproduced the expected phase structure but failed in the details. Our current simulations at $\beta=5.7$ on a $16^4$ lattice fail in similar ways while showing some improvement. We are therefore moving to even weaker couplings to see if the CLE might produce the correct results in the continuum (weak-coupling) limit, or, if it still fails, whether it might reproduce the results of the phase-quenched theory. We also discuss action (and other dynamics) modifications which might improve the performance of the CLE.Comment: Talk presented at Lattice 2017, Granada, Spain and submitted to proceedings. 8 pages, 4 figure