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 rea
l 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.
We consider thermodynamic singularities appearing in the complex chemical potential plane in the vicinity of QCD critical point. In order to investigate what the singularities are like in a concrete form, we resort to an effective theory based on a m
ean field approach. We study the behavior of extrema of the real part of the complex effective potential in the complex order parameter plane.
Two-color finite density QCD is free from the sign problem, and it is thus regarded as a good model to check the validity of the analytic continuation method. We study the method in terms of the corresponding chiral random matrix model. It is found t
hat at temperatures slightly higher than the pseudo critical temperature, the ratio type of extrapolated function works well in accordance with the results of the Monte Carlo simulations.
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 l
attice field theory with the $theta$ term. We reconsider this problem from the point of view of the maximum entropy method.
Lattice field theory with the $theta$ term suffers from the sign problem. The sign problem appears as flattening of the free energy. As an alternative to the conventional method, the Fourier transform method (FTM), we apply the maximum entropy me
thod (MEM) to Monte Carlo data obtained using the CP$^3$ model with the $theta$ term. For data without flattening, we obtain the most probable images of the partition function ${hat{cal Z}}(theta)$ with rather small errors. The results are quantitatively close to the result obtained with the FTM. Motivated by this fact, we systematically investigate flattening in terms of the MEM. Obtained images ${hat{cal Z}}(theta)$ are consistent with the FTM for small values of $theta$, while the behavior of ${hat{cal Z}}(theta)$ depends strongly on the default model for large values of $theta$. This behavior of ${hat{cal Z}}(theta)$ reflects the flattening phenomenon.
The weak coupling region of CP$^{N-1}$ lattice field theory with the $theta$-term is investigated. Both the usual real theta method and the imaginary theta method are studied. The latter was first proposed by Bhanot and David. Azcoiti et al. proposed
an inversion approach based on the imaginary theta method. The role of the inversion approach is investigated in this paper. A wide range of values of $h=-{rm Im} theta$ is studied, where $theta $ denotes the magnitude of the topological term. Step-like behavior in the $x$-$h$ relation (where $x=Q/V$, $Q$ is the topological charge, and $V$ is the two dimensional volume) is found in the weak coupling region. The physical meaning of the position of the step-like behavior is discussed. The inversion approach is applied to weak coupling regions.
The sign problem is notorious in Monte Carlo simulations of lattice QCD with the finite density, lattice field theory (LFT) with a $theta$ term and quantum spin models. In this report, to deal with the sign problem, we apply the maximum entropy met
hod (MEM) to LFT with the $theta$ term and investigate to what extent the MEM is applicable to this issue. Based on this study, we also make a brief comment about lattice QCD with the finite density in terms of the MEM.
We study the sign problem in lattice field theory with a $theta$ term. We apply the maximum entropy method (MEM) to flattening phenomenon of the free energy density $f(theta)$, which originates from the sign problem. In our previous paper, we applied
the MEM by employing the Gaussian topological charge distribution $P(Q)$ as mock data. In the present paper, we consider models in which `true flattening of $f(theta)$ occurs. These may be regarded as good examples for studying whether the MEM could correctly detect non trivial phase structure.
We study the sign problem in lattice field theory with a $theta$ term, which reveals as flattening phenomenon of the free energy density $f(theta)$. We report the result of the MEM analysis, where such mock data are used that `true flattening of $f(t
heta)$ occurs. This is regarded as a simple model for studying whether the MEM could correctly detect non trivial phase structure in $theta$ space. We discuss how the MEM distinguishes fictitious and true flattening.
A $theta$ term in lattice field theory causes the sign problem in Monte Carlo simulations. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. This strategy, however, has a limitation, because errors o
f $P(Q)$ prevent one from calculating the partition function ${cal Z}(theta)$ properly for large volumes. This is called flattening. As an alternative approach to the Fourier method, we utilize the maximum entropy method (MEM) to calculate ${cal Z}(theta)$. We apply the MEM to Monte Carlo data of the CP$^3$ model. It is found that in the non-flattening case, the result of the MEM agrees with that of the Fourier transform, while in the flattening case, the MEM gives smooth ${cal Z}(theta)$.
