Singularities of QCD in the complex chemical potential plane

We study the thermodynamic singularities of QCD in the complex chemical potential plane by a numerical simulation of lattice QCD, and discuss a method to understand the nature of the QCD phase transition at finite density from the information of the singularities. The existence of singular points at which the partition function (Z) vanishes is expected in the complex plane. These are called Lee-Yang zeros or Fisher zeros. We investigate the distribution of these singular points using the data obtained by a simulation of two-flavor QCD with p4-improved staggered quarks. The convergence radius of a Taylor expansion of ln Z in terms of the chemical potential is also discussed.Comment: 7 pages, 7 figures, Contribution to the "XXVII International Symposium on Lattice Field Theory", July 26-31, 2009, Peking University, Beijing, Chin

Two dimensional CP^2 Model with \theta-term and Topological Charge Distributions

Topological charge distributions in 2 dimensional CP^2 model with theta-term is calculated. In strong coupling regions, topological charge distribution is approximately given by Gaussian form as a function of topological charge and this behavior leads to the first order phase transition at \theta=\pi. In weak coupling regions it shows non-Gaussian distribution and the first order phase transition disappears. Free energy as a function of \theta shows "flattening" behavior at theta=theta_f<pi, when we calculate the free energy directly from topological charge distribution. Possible origin of this flattening phenomena is prensented.Comment: 17 pages,7 figure

Complex singularities around the QCD critical point at finite densities

Partition function zeros provide alternative approach to study phase structure of finite density QCD. The structure of the Lee-Yang edge singularities associated with the zeros in the complex chemical potential plane has a strong influence on the real axis of the chemical potential. In order to investigate what the singularities are like in a concrete form, we resort to an effective theory based on a mean field approach in the vicinity of the critical point. The crossover is identified as a real part of the singular point. We consider the complex effective potential and explicitly study the behavior of its extrema in the complex order parameter plane in order to see how the Stokes lines are associated with the singularity. Susceptibilities in the complex plane are also discussed.Comment: LaTeX, 27 pages with 15 figure

Lattice Field Theory with the Sign Problem and the Maximum Entropy Method

Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the $\theta$ term. We reconsider this problem from the point of view of the maximum entropy method.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Maximum Entropy Method Approach to θ\theta Term

In Monte Carlo simulations of lattice field theory with a $\theta$ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution $P(Q)$. This procedure, however, causes flattening phenomenon of the free energy $f(\theta)$, which makes study of the phase structure unfeasible. In order to treat this problem, we apply the maximum entropy method (MEM) to a Gaussian form of $P(Q)$, which serves as a good example to test whether the MEM can be applied effectively to the $\theta$ term. We study the case with flattening as well as that without flattening. In the latter case, the results of the MEM agree with those obtained from the direct application of the Fourier transform. For the former, the MEM gives a smoother $f(\theta)$ than that of the Fourier transform. Among various default models investigated, the images which yield the least error do not show flattening, although some others cannot be excluded given the uncertainty related to statistical error.Comment: PTPTEX , 25 pages with 11 figure