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

A method to study complex systems of mesons in Lattice QCD

Finite density systems can be explored with Lattice QCD through the calculation of multi-hadron correlation functions. Recently, systems with up to 12 $\pi^+$'s or $K^+$'s have been studied to determine the 3-$\pi^+$ and 3-$K^+$ interactions, and the corresponding chemical potentials have been determined as a function of density. We derive recursion relations between correlation functions that allow this work to be extended to systems of arbitrary numbers of mesons and to systems containing many different types of mesons, such as $\pi^+$'s, $K^+$'s, $\bar{D}^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and for the study of high-density systems.Comment: JLAB-THY-10-1121, NT@UW-10-01, journal versio

Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD

We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, \bra\Delta H^2\ket^{1/2}, is about 10 times smaller than that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al., and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in Quantum Monte Carlo.Comment: 14 pages, 6 figure

A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix simulations of a two-matrix model at nonzero chemical potential. The sign problem, caused by the complex fermion determinants, is solved by gathering the matrices into subsets, whose sums of determinants are real and positive even though their cardinality only grows linearly with the matrix size. A detailed proof of this positivity theorem is given for an arbitrary number of fermion flavors. We performed importance sampling Monte Carlo simulations to compute the chiral condensate and the quark number density for varying chemical potential and volume. The statistical errors on the results only show a mild dependence on the matrix size and chemical potential, which confirms the absence of sign problem in the subset method. This strongly contrasts with the exponential growth of the statistical error in standard reweighting methods, which was also analyzed quantitatively using the subset method. Finally, we show how the method elegantly resolves the Silver Blaze puzzle in the microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references; in Sec. VB: added discussion of model satisfying the Silver Blaze for all N (proof in Appendix E

Algorithm Shootout: R versus RHMC

We present initial results comparing the RHMC and R algorithms on large lattices with small quark masses using chiral fermions. We also present results concerning staggered fermions near the deconfinement/chiral phase transition. We find that the RHMC algorithm not only eliminates the step-size error of the R algorithm, but is also considerably more efficient. We discuss several possibilities for further improvement to the RHMC algorithm.Comment: Proceedings from Lattice 2005 (Dublin

General heatbath algorithm for pure lattice gauge theory

A heatbath algorithm is proposed for pure SU(N) lattice gauge theory based on the Manton action of the plaquette element for general gauge group N. Comparison is made to the Metropolis thermalization algorithm using both the Wilson and Manton actions. The heatbath algorithm is found to outperform the Metropolis algorithm in both execution speed and decorrelation rate. Results, mostly in D=3, for N=2 through 5 at several values for the inverse coupling are presented.Comment: 9 pages, 10 figures, 1 table, major revision, final version, to appear in PR

Some Insights into the Method of Center Projection

We present several new results which pertain to the successes of center projection in maximal center gauge (MCG). In particular, we show why any center vortex, inserted "by hand" into a thermalized lattice configuration, will be among the set of vortices found by the center projection procedure. We show that this "vortex-finding property" is lost when gauge-field configurations are fixed to Landau gauge prior to the maximal center gauge fixing; this fact accounts for the loss of center dominance in the corresponding projected configurations. Variants of maximal center (adjoint Landau) gauge are proposed which correctly identify relevant center vortices.Comment: LATTICE99(confine), 3 pages, 3 figure

Noisy Monte Carlo revisited

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. Our algorithm, simplified from that of L. Lin et al. hep-lat/9905033, avoids the computation of almost all non-leading terms. We illustrate its use by simulating SU(2) lattice gauge theory with a 5-loop action, and discuss further applications to full QCD.Comment: latex, 8 page

Probing the QCD vacuum with an abelian chromomagnetic field: A study within an effective model

We study the response of the QCD vacuum to an external abelian chromomagnetic field in the framework of a non local Nambu-Jona Lasinio model with the Polyakov loop. We use the Lattice results on the deconfinement temperature of the pure gauge theory to compute the same quantity in the presence of dynamical quarks. We find a linear relationship between the deconfinement temperature with quarks and the squared root of the applied field strength, $gH$, in qualitative (and to some extent also quantitative) agreement with existing Lattice calculations. On the other hand, we find a discrepancy on the approximate chiral symmetry restoration: while Lattice results suggest the deconfinement and the chiral restoration remain linked even at non-zero value of $gH$, our results are consistent with a scenario in which the two transitions are separated as $gH$ is increased.Comment: 14 pages, 7 figures, RevTeX4. Published version, with enlarged abstract and minor changes in the main tex

Electromagnetic properties of strange baryons in a relativistic quark model

We present some of our results for the electromagnetic properties of excited Σ hyperons, computed within the framework of the Bonn constituent-quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model are fitted against the best-known baryon masses. Accordingly, the results for the form factors and helicity amplitudes are genuine predictions. We compare with the scarce experimental data available and discuss the processes in which Σ *'s may play an important role