We study properties of SU(2) Yang-Mills theory on a four-dimensional Euclidean spacetime in which two directions are compactified into a finite two-dimensional torus T2 while two others constitute a ...large R2 subspace. This Euclidean T2×R2 manifold corresponds simultaneously to two systems in a (3+1) dimensional Minkowski spacetime: a zero-temperature theory with two compactified spatial dimensions and a finite-temperature theory with one compactified spatial dimension. Using numerical lattice simulations we show that the model exhibits two phase transitions related to the breaking of center symmetries along the compactified directions. We find that at zero temperature the transition lines cross each other and form the Greek letter γ in the phase space parametrized by the lengths of two compactified spatial dimensions. There are four different phases. We also demonstrate that the compactification of only one spatial dimension enhances the confinement property and, consequently, increases the critical deconfinement temperature.
We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number ...density for imaginary chemical potential iμqI. Then we restore the grand canonical partition function for imaginary chemical potential using the fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using the known method of the hopping parameter expansion and compare results obtained by two methods in the deconfining as well as in the confining phases. The agreement between two methods indicates the validity of the new method. Our numerical results are obtained in two flavor lattice QCD with clover improved Wilson fermions.
We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, 〈n〉, are calculated at the pure imaginary chemical potential iμqI, where no sign problem occurs. Then, ...the canonical partition functions, ZC(n,T,V), up to some maximal values of n are estimated through fitting theoretically motivated functions to 〈n〉, which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T/Tc=0.84-1.35.
In the distributions of the Lee-Yang zeros, we observe the Roberge-Weiss phase transition at T/Tc≥1.20. We discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n, so that we can estimate a reliable infinite volume limit.
Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum. The current may be produced either ...in an unbounded curved spacetime or in a flat spacetime in a physically bounded system. In both cases, the magnitude of the electric current is proportional to the beta-function associated with renormalization of the electric charge. In our article, we investigate the electric current density induced by the magnetic field in the vicinity of a Dirichlet boundary in the scalar QED. Using first-principle lattice simulations we show that the electric current, generated by this “conformal magnetic effect at the edge” (CMEE), is well described by the conformal anomaly provided the conformal symmetry is classically unbroken. Outside of the conformal limit, the current density is characterized by an anomalous power law near the edge of the system and by an exponential suppression of the current far away from the edge.
A
bstract
The phase diagram of two-color QCD with non-zero chiral chemical potential is studied by means of lattice simulation. We focus on the influence of a chiral chemical potential on the ...confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulation is carried out with dynamical staggered fermions without rooting. The dependences of the Polyakov loop, the chiral condensate and the corresponding susceptibilities on the chiral chemical potential and the temperature are presented. The critical temperature is observed to increase with increasing chiral chemical potential.
A novel approach to the problem of deriving the generating functional for the canonical ensemble in lattice QCD at a nonzero chemical potential is proposed. The derivation proceeds in several steps. ...First, the baryon density for imaginary values of the chemical potential is obtained. Then, again for imaginary values of the chemical potential, the generating functional of the grand canonical ensemble is derived. In this analysis, a fit of baryon density is employed toward simplifying the procedure of numerical integration. Finally, the generating potential for the canonical ensemble is derived using a high-precision numerical Fourier transform. The generating functional for the canonical ensemble is also derived using the known hopping-parameter expansion, and the results obtained with the two methods are compared for the deconfinement phase in the lattice QCD with two flavors.
Roberge–Weiss Transition in the Lee–Yang Approach Rogalev, R. N.; Bornyakov, V. G.; Gerasimeniuk, N. V. ...
Physics of particles and nuclei letters,
06/2023, Letnik:
20, Številka:
3
Journal Article
Recenzirano
Thermodynamic quantities characterizing dense and hot strongly interacting matter have been studied in the lattice regularization of QCD with two flavors in the Lee–Yang approach. It is shown that, ...at high temperatures and taking into account a sufficiently large number of fermionic modes, Lee–Yang zeros in the complex plane of baryon fugacity lie on the negative real semiaxis, which corresponds to the Roberge–Weiss transition. On the line of Lee–Yang zeros, the baryon density and pressure have a gap; it is shown that the baryon density jump is proportional to the density of Lee–Yang zeros. Two methods for calculating baryon number distributions are considered; it is shown that the method based on the asymptotic estimate gives only positive state probabilities with a certain baryon number, as opposed to numerical integration. The importance of experimental measurements of these probabilities to study the issue of achieving thermodynamic equilibrium in nuclear-nuclear collisions is discussed.
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