How to get from imaginary to real chemical potential

Using the exactly solvable Gross-Neveu model as theoretical laboratory, we analyse in detail the relationship between a relativistic quantum field theory at real and imaginary chemical potential. We find that one can retrieve the full information about the phase diagram of the theory from an imaginary chemical potential calculation. The prerequisite is to evaluate and analytically continue the effective potential for the chiral order parameter, rather than thermodynamic observables or phase boundaries. In the case of an inhomogeneous phase, one needs to compute the full effective action, a functional of the space-dependent order parameter, at imaginary chemical potential.Comment: revtex, 9 pages, 10 figures; v2: add more references, modify concluding sectio

The phase diagram of QCD with four degenerate quarks

We revisit the determination of the pseudo-critical line of QCD with four degenerate quarks at non-zero temperature and baryon density by the method of analytic continuation. We determine the pseudo-critical couplings at imaginary chemical potentials by high-statistics Monte Carlo simulations and reveal deviations from the simple quadratic dependence on the chemical potential visible in earlier works on the same subject. Finally, we discuss the implications of our findings for the shape of the pseudo-critical line at real chemical potential, comparing different possible extrapolations.Comment: 8 pages, 8 figures, 2 table

Critical point of Nf=3N_f = 3 QCD from lattice simulations in the canonical ensemble

A canonical ensemble algorithm is employed to study the phase diagram of $N_f = 3$ QCD using lattice simulations. We lock in the desired quark number sector using an exact Fourier transform of the fermion determinant. We scan the phase space below $T_c$ and look for an S-shape structure in the chemical potential, which signals the coexistence phase of a first order phase transition in finite volume. Applying Maxwell construction, we determine the boundaries of the coexistence phase at three temperatures and extrapolate them to locate the critical point. Using an improved gauge action and improved Wilson fermions on lattices with a spatial extent of 1.8 \fm and quark masses close to that of the strange, we find the critical point at $T_E = 0.925(5) T_c$ and baryon chemical potential $\mu_B^E = 2.60(8) T_c$.Comment: 5 pages, 7 figures, references added, published versio

The critical line from imaginary to real baryonic chemical potentials in two-color QCD

The method of analytic continuation from imaginary to real chemical potentials $\mu$ is one of the few available techniques to study QCD at finite temperature and baryon density. One of its most appealing applications is the determination of the critical line for small $\mu$: we perform a direct test of the validity of the method in this case by studying two-color QCD, where the sign problem is absent. The (pseudo)critical line is found to be analytic around $\mu^2 = 0$, but a very large precision would be needed at imaginary $\mu$ to correctly predict the location of the critical line at real $\mu$.Comment: Replaced with the version accepted for publication as a Rapid Communication in Physical Review D

Confining strings in representations with common nn-ality

We study the spectrum of confining strings in SU(3) pure gauge theory, by means of lattice Monte Carlo simulations, using torelon operators in different representations of the gauge group. Our results provide direct evidence that the string spectrum is according to predictions based on $n$-ality. Torelon correlations in the rank-2 symmetric channel appear to be well reproduced by a two-exponential picture, in which the lowest state is given by the fundamental string $\sigma_1=\sigma$, the heavier string state is such that the ratio $\sigma_2/\sigma_1$ is approximately given by the Casimir ratio $C_{\rm sym}/C_{\rm f} = 5/2$, and the torelon has a much smaller overlap with the lighter fundamental string state.Comment: 7 pages, 2 figure

EoS of finite density QCD with Wilson fermions by Multi-Parameter Reweighting and Taylor expansion

The equation of state (EoS), quark number density and susceptibility at nonzero quark chemical potential $\mu$ are studied in lattice QCD simulations with a clover-improved Wilson fermion of 2-flavors and RG-improved gauge action. To access nonzero $\mu$, we employ two methods : a multi-parameter reweighting (MPR) in $\mu$ and $\beta$ and Taylor expansion in $\mu/T$. The use of a reduction formula for the Wilson fermion determinant enables to study the reweighting factor in MPR explicitly and heigher-order coefficients in Taylor expansion free from errors of noise method, although calculations are limited to small lattice size. As a consequence, we can study the reliability of the thermodynamical quantities through the consistency of the two methods, each of which has different origin of the application limit. The thermodynamical quantities are obtained from simulations on a $8^3\times 4$ lattice with an intermediate quark mass($m_{\rm PS}/m_{\rm V}=0.8)$. The MPR and Taylor expansion are consistent for the EoS and number density up to $\mu/T\sim 0.8$ and for the number susceptibility up to $\mu/T \sim 0.6$. This implies within a given statistics that the overlap problem for the MPR and truncation error for the Taylor expansion method are negligible in these regions. In order to make MPR methods work, the fluctuation of the reweighting factor should be small. We derive the equation of the reweighting line where the fluctuation is small, and show that the equation of the reweighting line is consistent with the fluctuation minimum condition.Comment: 20 pages, 11 figures. Accepted to JHEP. Discussions are added. Figures for Taylor coefficients (Fig. 7) are modifie

Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential

We demonstrate analytically that complex Langevin dynamics can solve the sign problem in one-dimensional QCD in the thermodynamic limit. In particular, it is shown that the contributions from the complex and highly oscillating spectral density of the Dirac operator to the chiral condensate are taken into account correctly. We find an infinite number of classical fixed points of the Langevin flow in the thermodynamic limit. The correct solution originates from a continuum of degenerate distributions in the complexified space.Comment: 20 pages, several eps figures, minor comments added, to appear in JHE

Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity

We investigate an ultracold Fermi gas at unitarity confined in a periodic box $V=L^3$ using renormalization group (RG) techniques. Within this approach we can quantitatively assess the long range bosonic order parameter fluctuations which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finite-size and particle-number effects present in Monte-Carlo simulations of ultracold Fermi gases.Comment: 13 pages, 7 figure

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange

EurA1c: the European HbA1c Trial to Investigate the Performance of HbA1c Assays in 2166 Laboratories across 17 Countries and 24 Manufacturers by Use of the IFCC Model for Quality Targets

Background: A major objective of the IFCC Committee on Education and Use of Biomarkers in Diabetes is to generate awareness and improvement of HbA1c assays through evaluation of the performance by countries and manufacturers. Methods: Fresh whole blood and lyophilized hemolysate specimens manufactured from the same pool were used by 17 external quality assessment organizers to evaluate analytical performance of 2166 laboratories. Results were evaluated per country, per manufacturer, and per manufacturer and country combined according to criteria of the IFCC model for quality targets. Results: At the country level with fresh whole blood specimens, 6 countries met the IFCC criterion, 2 did not, and 2 were borderline. With lyophilized hemolysates, 5 countries met the criterion, 2 did not, and 3 were borderline. At the manufacturer level using fresh whole blood specimens, 13 manufacturers met the criterion, 8 did not, and 3 were borderline. Using lyophilized hemolysates, 7 manufacturers met the criterion, 6 did not, and 3 were borderline. In both country and manufacturer groups, the major contribution to total error derived from between-laboratory variation. There were no substantial differences in performance between groups using fresh whole blood or lyophilized hemolysate samples. Conclusions: The state of the art is that 1 of 20 laboratories does not meet the IFCC criterion, but there are substantial differences between country and between manufacturer groups. Efforts to further improve quality should focus on reducing between-laboratory variation. With some limitations, fresh whole blood and well-defined lyophilized specimens are suitable for purpose