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Register a new userSingularities around the QCD critical point in the complex chemical potential plane
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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 mean field approach. We study the behavior of extrema of the real part of the complex effective potential in the complex order parameter plane.
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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.
Finite-size scaling is investigated in detail around the critical point in the heavy-quark region of nonzero temperature QCD. Numerical simulations are performed with large spatial volumes up to the aspect ratio $N_s/N_t=12$ at a fixed lattice spacing with $N_t=4$. We show that the Binder cumulant and the distribution function of the Polyakov loop follow the finite-size scaling in the $Z(2)$ universality class for large spatial volumes with $N_s/N_t ge 9$, while, for $N_s/N_t le 8$, the Binder cumulant becomes inconsistent with the $Z(2)$ scaling. To realize the large-volume simulations in the heavy-quark region, we adopt the hopping tails expansion for the quark determinant: We generate gauge configurations using the leading order action including the Polyakov loop term for $N_t=4$, and incorporate the next-to-leading order effects in the measurements by the multipoint reweighting method. We find that the use of the leading-order configurations is crucially effective in suppressing the overlapping problem in the reweighting and thus reducing the statistical errors.
We investigate the phase structure of three-flavor QCD in the presence of finite quark chemical potential $mu/Tlesssim1.2$ by using the non-perturbatively $O(a)$ improved Wilson fermion action on lattices with a fixed temporal extent $N_{rm t}=6$ and varied spatial linear extents $N_{rm s}=8,10,12$. Especially, we focus on locating the critical end point that characterizes the phase structure, and extracting the curvature of the critical line on the $mu$-$m_{pi}$ plane. For Wilson-type fermions, the correspondence between bare parameters and physical parameters is indirect. Hence we present a strategy to transfer the bare parameter phase structure to the physical one, in order to obtain the curvature. Our conclusion is that the curvature is positive. This implies that, if one starts from a quark mass in the region of crossover at zero chemical potential, one would encounter a first-order phase transition when one raises the chemical potential.
We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.
Within the reweighting approach, one has the freedom to choose the Monte Carlo action so that it provides a good overlap with the finite-mu measure but remains simple to simulate. We explore several choices of action in the regime of small mu. Simulating with a finite isospin chemical potential mu_I=mu gives a better overlap than the standard choice mu=0, with no computational overhead.
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