Meson Effects on the Chiral Condensate at Finite Density

Meson corrections on the chiral condensate up to next-to-leading order in a 1/Nc expansion at finite densityare investigated in the NJL model with explicit chiral symmetry breaking. Compared with mean-field results, the chiralphase transition is still of the first order while the properties near the critical density for chiral phase transition are foundto change significantly.     

The chiral phase transition at high baryon density from nonperturbative flow equations

We investigate the chiral phase transition at high baryon number density within the linear quark meson model for two flavors. The method we employ is based on an exact renormalization group equation for the free energy. Truncated nonperturbative flow equations are derived at nonzero chemical potential and temperature. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, we find a chiral symmetry restoring first order transition at high density. Combined with previous investigations at nonzero temperature, the result implies the presence of a tricritical point with long–range correlations in the phase diagram. Received: 24 August 1999 / Published online: 17 February 2000     

Phase structure of two-flavor QCD at finite chemical potential

We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.     

带有2+1味道Wilson费米子的格点量子色动力学在有限温度、有限密度下的相变

利用格点规范理论研究了带有2＋1味道费米子的量子色动力学在有限密度及温度下的相变问题,研究了去禁闭相变与化学势和裸质量参数之间的依赖关系,并利用有限体积效应分析以及Monte Carlo模拟的演化序列所反映出的特点对相变的类型做了确认,给出了相结构图. 关键词： 格点量子色动力学 相变     

QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

The chiral and deconfinement phase transitions

By introducing the dressed Polayakov loop or dual chiral condensate as a candidate order parameter to describe the deconfinement phase transition for light flavors, we discuss the interplay between the chiral and deconfinement phase transitions, and propose the possible QCD phase diagram at finite temperature and density. We also introduce a dynamical gluodynamic model with dimension-2 gluon condensate, which can describe the color electric deconfinement as well as the color magnetic confinement.     

利用格点量子色动力学研究手征平滑过渡温度和手征相变温度

回顾了最近关于手征平滑过渡温度和手征相变温度的研究结果。首先给出了在零重子化学势能下的手征平滑过渡温度为156.5(1.5) MeV,其次,给出了在非零重子化学势能下手征相转变曲线的二阶及四阶曲率分别为0.012(4)和0.000(4)。接着讨论了在格点QCD中第一次得到的量子色动力学的手征相变温度。在热力学极限、连续极限及手征极限下,我们得到手征相变温度为132$^{+3}_{-6}$ MeV。     

On the chiral phase transition in hadronic matter

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and nonzero baryon density is performed. It is assumed that, at zero baryonic density, ρ=0, the temperature phase transition is of the second order. Due to a specific power dependence of baryon masses on the chiral condensate, the phase transition becomes of the first order at the temperature T=T_ph(ρ) for ρ>0. At temperatures T_cont(ρ)> _T>_Tph(ρ), there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature T=T_cont(ρ), the system experiences a continuous transition to the pure chirally symmetric phase.     

Equation of State of the Strong Interaction Matter in an External Magnetic Field

We investigate the equation of state of the strong interaction matter in a background magnetic field via the two flavor Nambu-Jona-Lasinio model. Starting from the mean-field thermodynamical potential density Ω, we calculate the pressure density p, the entropy density s, the energy density ε, and the interaction measure (ε-3p)=T⁴ of the strong interaction matter at finite temperature and finite magnetic field. The results manifest that the chiral phase transition is just a crossover but not a low order phase transition. Moreover there may exist magnetic catalysis effect, and its mechanism is just the effective dimension reduction induced by the magnetic field.     

Critical properties of XY model on two-layer Villain－ferromagnetic lattice

We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane (J) and a ferromagnetic plane (I), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters (I,J), the system presents three phases: namely, a Kosterlitz－Thouless (KT) phase in which the two planes are critical for I predominant over J, a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of (I,J): the KT transition, the Ising transition and an XY-Ising transition with ν=0.849(3). It turns out that the Ising or XY-Ising transition is associated with the disappearance of the chiral order in the Villain plane.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Confining but chirally symmetric dense and cold matter

The possibility for existence of cold, dense chirally symmetric matter with confinement is reviewed. The answer to this question crucially depends on the mechanism of mass generation in QCD and interconnection of confinement and chiral symmetry breaking. This question can be clarified from spectroscopy of hadrons and their axial properties. Almost systematical parity doubling of highly excited hadrons suggests that their mass is not related to chiral symmetry breaking in the vacuum and is approximately chirally symmetric. Then there is a possibility for existence of confining but chirally symmetric matter. We clarify a possible mechanism underlying such a phase at low temperatures and large density. Namely, at large density the Pauli blocking prevents the gap equation to generate a solution with broken chiral symmetry. However, the chirally symmetric part of the quark Green function as well as all color non-singlet quantities are still infrared divergent, meaning that the system is with confinement. A possible phase transition to such a matter is most probably of the first order. This is because there are no chiral partners to the lowest lying hadrons.     

Effects of the anomaly on the two-flavor QCD chiral phase transition

We use strongly coupled lattice QED with two flavors of massless staggered fermions to model the chiral phase transition in two-flavor massless QCD. Our model allows us to vary the QCD anomaly and thus study its effects on the transition. Our study confirms the widely accepted viewpoint that the chiral phase transition is first order in the absence of the anomaly. Turning on the anomaly weakens the transition and turns it second order at a critical anomaly strength. The anomaly strength at the tricritical point is characterized using r=(M(eta')-M(pi))/rho(eta'), where M(eta'), M(pi) are the screening masses of the anomalous and regular pions and rho(eta') is the mass scale that governs the low energy fluctuations of the anomalous symmetry. We estimate that r ~ 7 in our model. This suggests that a strong anomaly at the two-flavor QCD chiral phase transition is necessary to wash out the first order transition.     

A phenomenological theory of the isotropic to chiral smectic-C phase transition

In this paper we discuss the direct isotropic to chiral smectic-C phase transition on the basis of a phenomenological theory. The model free energy is written in terms of the coupled order parameters including the spontaneous polarization. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a direct isotropic to chiral smectic-C phase transition is possible when compared to other phase transitions. On the basis of this model the isotropic-smectic-C^* transition is always of first order. The theoretical predictions are compared with the available experimental results.-1     

Thermodynamics of chiral symmetry at low densities

The phase diagram of two-color QCD as a function of temperature and baryon chemical potential is considered. Using a low-energy chiral Lagrangian based on the symmetries of the microscopic theory, we determine, at the one-loop level, the temperature dependence of the critical chemical potential for diquark condensation and the temperature dependence of the diquark condensate and baryon density. The prediction for the temperature dependence of the critical chemical potential is consistent with the one obtained for a dilute Bose gas. The associated phase transition is shown to be of second order for low temperatures and first order at higher temperatures. The tricritical point at which the second order phase transition ends is determined. The results are carried over to QCD with quarks in the adjoint representation and to ordinary QCD at a non-zero chemical potential for isospin.     

The Equation of State and Phase Structure in A Model with Dynamical Spontaneous Symmetry Breaking at Finite Temperature and Density

Based on the Lurie model,a convenient scheme is constructed for calculating the equation of state approximately.The parametric equaion of state is given in the Lurie model.The phase diagram of the model shows the existence of critical point separating first order from second order chiral phase transition.The careful analysis of isotherms of pressure versus net baryon number density suggests the existence of overheat and overcool metastable state and the coexistence of broken phase and normal phase.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.