Evading the sign problem in random matrix simulations

We show how the sign problem occurring in dynamical simulations of random matrices at nonzero chemical potential can be avoided by judiciously combining matrices into subsets. For each subset the sum of fermionic determinants is real and positive such that importance sampling can be used in Monte Carlo simulations. The number of matrices per subset is proportional to the matrix dimension. We measure the chiral condensate and observe that the statistical error is independent of the chemical potential and grows linearly with the matrix dimension, which contrasts strongly with its exponential growth in reweighting methods.Comment: 4 pages, 3 figures, minor corrections, as published in Phys. Rev. Let

Towards a controlled study of the QCD critical point

The phase diagram of QCD, as a function of temperature T and quark chemical potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative nature makes it a natural object of lattice studies. However, the sign problem prevents the application of standard Monte Carlo techniques at non-zero baryon density. We have been pursuing an approach free of the sign problem, where the chemical potential is taken as imaginary and the results are Taylor-expanded in mu/T about mu=0, then analytically continued to real mu. Within this approach we have determined the sensitivity of the critical chemical potential mu_E to the quark mass, d(\mu_E)^2/dm_q|_{\mu_E=0}. Our study indicates that the critical point moves to {\em smaller} chemical potential as the quark mass {\em increases}. This finding, contrary to common wisdom, implies that the deconfinement crossover, which takes place in QCD at mu=0 when the temperature is raised, will remain a crossover in the mu-region where our Taylor expansion can be trusted. If this result, obtained on a coarse lattice, is confirmed by simulations on finer lattices now in progress, then we predict that no {\em chiral} critical point will be found for mu_B \lesssim 500 MeV, unless the phase diagram contains additional transitions.Comment: 4 pages, 6 figures, proceedings of Quark Matter 2008, Jaipur (India), Feb. 2008, to appear in J. Phys.

Strange mass dependence of the tricritical point in the U(3)_L x U(3)_R chiral sigma model

We study the strange quark mass dependence of the tricritical point of the U(3)_L x U(3)_R linear sigma model in the chiral limit. Assuming that the tricritical point is at a large strange mass value, the strange sector as well as the \eta-a_0 sector decouples from the light degrees of freedom which determines the thermodynamics. By tracing this decoupling we arrive from the original U(3)_L x U(3)_R symmetric model, going through the U(2)_L x U(2)_R symmetric one, at the SU(2)_L x SU(2)_R linear sigma model. One-loop level beta functions for the running of the parameters in each of these models and tree-level matching of the coupling of these models performed at intermediate scales are used to determine the influence of the heavy sector on the parameters of the SU(2)_L x SU(2)_R linear sigma model. By investigating the thermodynamics of this latter model we identified the tricritical surface of the U(3)_L x U(3)_R linear sigma model in the chiral limit. To apply the results for QCD we used different scenarios for the m_s and \mu_q dependence of the effective model parameters, then the \mu_q^TCP(m_s) function can be determined. Depending on the details, a curve bending upwards or downwards near \mu_q=0 can be obtained, while with explicit chemical potential dependence of the parameters the direction of the curve can change with m_s, too.Comment: 17 pages, 6 figures, uses revtex4-

Model analysis of thermal UV-cutoff effects on the chiral critical surface at finite temperature and chemical potential

We study the effects of temporal UV-cutoff on the chiral critical surface in hot and dense QCD using a chiral effective model. Recent lattice QCD simulations indicate that the curvature of the critical surface might change toward the direction in which the first order phase transition becomes stronger on increasing the number of lattice sites. To investigate this effect on the critical surface in an effective model approach, we use the Nambu-Jona-Lasinio model with finite Matsubara frequency summation. We find that qualitative feature of the critical surface does not alter appreciably as we decrease the summation number, which is unlike the case what is observed in the recent lattice QCD studies. This may either suggest the dependence of chemical potential on the coupling strength or due to some additional interacting terms such as vector interactions which could play an important role at finite density.Comment: 7 pages, 8 figure

QCD phase diagram for small densities from simulations at imaginary mu

We present results on the QCD phase diagram for small densities without reweighting. Our simulations are performed with an imaginary chemical potential mu_I for which the fermion determinant is positive. On an 8^3x4 lattice with 2 flavors of staggered quarks, we map out the pseudo-critical temperature T_c(mu_I). For mu_I/T < pi/3, this is an analytic function whose Taylor expansion converges rapidly, with truncation errors smaller than statistical ones. The result is analytically continued to give the location of the pseudo-critical line for real mu_B<500 MeV.Comment: Lattice2002(nonzerot), 3 pp, 5 figure

Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

We present unambiguous evidence from lattice simulations of QCD with three degenerate quark species for two tricritical points in the (T,m) phase diagram at fixed imaginary \mu/T=i\pi/3 mod 2\pi/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary chemical potential, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to non-degenerate and light quark masses is discussed.Comment: 4 pages, 5 figure

Improved AdS/QCD Model with Matter

We study an improved AdS/QCD model at finite temperature and chemical potential. An Ansatz for the beta-function for the boundary theory allows for the derivation of a charged dilatonic black hole in bulk. The solution is asymptotically RN-AdS in the UV and AdS2 * R3 in the IR. We discuss the thermodynamical aspects of the solution. The fermionic susceptibilities are shown to deviate from the free fermionic limits at asymptotic temperatures despite the asymptotically free nature of the gauge coupling at the boundary. The Polyakov line, the temporal and spatial string tensions dependence on both temperature and chemical potential are also discussed

Lattice baryons in the 1/N expansion

Results are presented for hadron spectroscopy with gauge groups SU(N) with N=3, 5, 7. Calculations use the quenched approximation. Lattice spacings are matched using the static potential. Meson spectra show independence on N and vacuum-to-hadron matrix elements scale as the square root of N. The baryon spectrum shows the excitation levels of a rigid rotor.Comment: 19 pages, 11 figure

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.

Degrees of freedom and the phase transitions of two flavor QCD

We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the linear sigma model extended by including a Polyakov loop potential, which is fitted to reproduce pure gauge theory thermodynamics, and a coupling between the chiral fields and the Polyakov loop. Thus the resulting models have as relevant degrees of freedom the Polyakov loop and chiral fields. By comparing the extended models with the bare chiral models we can conclude that the addition of the Polyakov loop is necessary in order to obtain both qualitatively and quantitatively correct results at finite temperatures. These results are extended to finite net quark densities, several thermodynamical quantites are investigated in detail and possible applications and consequences for relativistic heavy ion collision phenomenology are discussed