Chiral Order Parameter Research Articles

Chirality measure and chiral order parameter for a two-dimensional system

A chirality measure and a chiral order parameter are defined for two-dimensional systems based upon the transformation properties of pseudotensors. The quantities are derived by considering the polarization induced by an electric field applied normal to a system comprising a vacuum above an inhomogeneous dielectric bounded by a plane surface. The quantities are defined by analogy to the three-dimensional case which has been considered by the authors previously. The index is illustrated by a calculation of the chiral order parameter for an Archimedean spiral structure.

A MATHEMATICAL MODEL OF SURFACE-PRESSURE-INDUCED SEPARATION OF CHIRAL PHASES IN MONOLAYER OF RACEMIC AMPHIPHILES AND ITS CLASSICAL SOLUTIONS IN TWO-DIMENSIONAL CASE

The problem of the surface-pressure-induced separation of chiral phases in monolayer of racemic amphiphiles is studied.Following the work of Ou-Yang and his co-wokers published in “Chem.Phys.Lett.(1998)”,we give several classes of classical solutions in the two-dimensional case for the equilibrium equations for the chiral phases separation order parameter and the molecular orientation pattern.

Nonequilibrium production of photons viaπ0→2γin disoriented chiral condensates

We study the production of photons via the nonequilibrium relaxation of a disoriented chiral condensate with the chiral order parameter having a large initial amplitude along the ${\ensuremath{\pi}}^{0}$ direction. Assuming the validity of the low-energy coupling of the neutral pion to photons via the U${}_{A}(1)$ anomalous vertex, we find that for large initial amplitudes along the ${\ensuremath{\pi}}^{0}$ direction photon production is enhanced by parametric amplification. These processes are nonperturbative with a large contribution during the nonequilibrium stages of the evolution and result in a distinct distribution of the produced photons and a polarization asymmetry. For initial amplitudes of the ${\ensuremath{\pi}}^{0}$ component of the order parameter between 200 and 400 MeV, corresponding to energy densities between 1 and 12 $\mathrm{GeV}/{\mathrm{fm}}^{3}$, we find a peak in the photon distribution at energies between $\ensuremath{\approx}300$ and 600 MeV. We also find polarization asymmetries typically between 5% and 10%. We discuss the potential experimental impact of these results as well as the problems associated with its detection.

Phase diagrams of the S= quantum antiferromagnetic XY model on the triangular lattice in magnetic fields

We study the S=1/2 quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins $N \leq 27$, and those at finite temperatures using a quantum transfer Monte Carlo method for $N \leq 24$. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3-plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.

QCD Sum Rules for Skeptics

A new Monte-Carlo based uncertainty analysis is introduced to quantitatively determine the predictive ability of QCD sum rules. A comprehensive analysis of ground stateρ-meson and nucleon spectral properties is performed. Many of the findings contradict the conventional wisdom of both practitioners and skeptics alike. Associations between the phenomenological fit parameters are particularly interesting as they reveal how the sum rules resolve the spectral properties. The use of derivative sum rules for the determination ofρ-meson spectral properties is shown to be a very unfavorable approach. Most prior nucleon sum rule analyses are based on a sum rule which is found to be invalid; the results are suspect, and should be reevaluated. The “Ioffe formula,” argued by many to qualitatively encapsulate a description of the nucleon mass in terms of the chiral symmetry breaking order parameter ⦠qq⦔ is misleading at best. QCD sum rules are found to be self-consistent without contributions from direct instantons. This implies that instanton effects are adequately accounted for in the nonperturbative vacuum condensates. This in-depth examination of QCD sum rule self consistency paints a favorable picture for further quantitative refinements of the QCD sum rule approach.

Scaling of Chiral Order Parameter in Two-Flavor QCD

The finite temperature transition of QCD with two degenerate light quarks is studied on the lattice with a renormalization group improved gauge action and the Wilson quark action. We have made simulations on an $8^3\times 4$ lattice near the chiral transition point. It is shown that the chiral condensate which is the order parameter of chiral symmetry satisfies remarkably a scaling relation with the exponents of the three dimensional O(4) Heisenberg model. This indicates that the chiral transition in two-flavor QCD is of second order in the continuum limit.

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.

Two-flavor staggered fermion thermodynamics at Nt=12.

We present results of an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date, approximately 0.1 fm. Of particular interest are (1) a study of the temperature of the crossover, an important indicator of continuum scaling, (2) a determination of the induced baryon charge and baryon susceptibility, used to study the dissolution of hadrons at the crossover, (3) the scalar susceptibility, a signal for the appearance of soft modes, and (4) the chiral order parameter, used to test models of critical behavior associated with chiral symmetry restoration. From our new data and published results for ${N}_{t}=4, 6, \mathrm{and} 8$, we determine the QCD magnetic equation of state from the chiral order parameter using O(4) and mean field critical exponents and compare it with the corresponding equation of state obtained from an O(4) spin model and mean field theory. We also present a scaling analysis of the Polyakov loop, suggesting a temperature-dependent constituent quark free energy.

Chiral symmetry restoration and [formula omitted]N symmetry

We demonstrate that chiral symmetry restoration in quenched finite temperature QCD depends crucially on the Z 3 phase of the Polyakov loop P . This dependence is a general consequence of the coupling of the chiral order parameter to the Polyakov loop. We construct a model for chiral symmetry breaking and restoration which includes the effect of a nontrivial Polyakov loop by calculating the effective potential for the chiral condensate of a Nambu-Jona-Lasinio model in a uniform temperature dependent A 0 gauge field background. Above the deconfinement temperature there are three possible phases corresponding to the Z 3 symmetric phases of the Polyakov loop in the pure gauge theory. In the phase in which tr c( P) is real and positive the first-order deconfining transition induces chiral symmetry restoration in agreement with simulation results. In the two phases where Re [tr c( P)] < 0 the sign of the leading finite temperature correction to the effective potential is reversed from the normal phase, and chiral symmetry is not restored at the deconfinement transition; this agrees with the recent simulation studies of Chandrasekharan and Christ. In the case of SU ( N) a rich set of possibilities emerges. The generality of the mechanism makes it likely to occur in full QCD as well; this will increase the lifetimes of metastable Z 3 phases.

Four-body chiral order parameters in the massless fermion phase.

The fermion four-point functions and condensates as the chiral symmetry order parameters are calculated analytically in U(1) gauge theory in the massless phase. It is shown that in leading order of the loop expansion of the effective action, there is a critical coupling for the nonperturbative parity-invariant chirality-changing four-fermion functions; this critical coupling however is the same as that for dynamical mass generation. Therefore there is no breaking of chiral symmetry through the condensation of four-fermion functions below the critical coupling for dynamical mass generation for the fermions.

The Gauged Thirring Model in 3+1 Dimensions

We propose the gauged Thirring model as a natural gauge-invariant generalization of the Thirring model, four-fermion interaction of current-current type. In the strong gauge-coupling limit, the gauged Thirring model reduces to the recently proposed reformulation of the Thirring model as a gauge theory. Especially, we pay attention to the effect coming from the kinetic term for the gauge boson field, which was originally the auxiliary field without the kinetic term. In 3 + 1 dimensions, we find the nontrivial phase structure for the gauged Thirring model, based on the Schwinger-Dyson equation for the fermion propagator as well as the gauge-invariant effective potential for the chiral order parameter. Within this approximation, we study the renormalization group flows (lines of constant physics) and find a signal for nontrivial continuum limit with nonvanishing renormalized coupling constant and large anomalous dimension for the gauged Thirring model in 3+1 dimensions, at least for small number of flavors $N_f$. Finally we discuss the (perturbatively) renormalizable extension of the gauged Thirring model.

Two-flavor staggered-fermion thermodynamics at N t = 12

We present new results in an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover, an important indicator of continuum scaling, a determination of the induced baryon charge and baryon susceptibility, used to study the dissolution of hadrons at the crossover, the scalar susceptibility, a signal for the appearance of soft modes, and the chiral order parameter, used to test models of critical behavior.

Simple molecular model for induced cholesteric phases.

A phenomenological theory for the cholesteric phase induced by a chiral solute in a nematic solvent is derived from (i) the continuum representation of twist deformation of the nematic solvent, and (ii) the surface anchoring energy approximation for the interactions between the solvent and a solute of given shape. This allows a simple explanation of the stabilization of the solvent twist deformation by the interactions with chiral solute. A straightforward statistical elaboration leads to the well known inverse proportionality between the pitch of the cholesteric phase and the solute concentration. The corresponding proportionality coefficient, i.e., the twisting power of the solute, is then related to the asymmetry of the solute shape through a chirality order parameter. \textcopyright{} 1996 The American Physical Society.

The chiral condensate in nuclear matter

We investigate the density dependence of the chiral order parameter or quark condensate 〈 qq〉 in nuclear matter using relativistic Brueckner-Hartree-Fock theory. While the leading behavior linear in the density is known to be determined model independently by the pion-nucleon sigma term, we demonstrate that higher order corrections are extremely sensitive to the interpretation of the scalar “σ”-meson and its substructure.

Thirring model as a gauge theory

We give another reformulation of the Thirring model (with four-fern-don interaction of the current-current type) as a gauge theory and identify it with a gauge-fixed version of the corresponding gauge theory according to the Batalin-Fradkin formalism. Based on this formalism, we study the chiral symmetry breaking of the D-dimensional Thirring model (2 < D < 4) with N flavors of 4-component fermions. By constructing the gauge covariant effective potential for the chiral order parameter, up to the leading order of 1/ N expansion, we show the existence of the second order chiral phase transition and obtain explicitly the critical number of flavors N c (respectively critical four-fermion coupling G c ) as a function of the four-fermion coupling G(respectively N), below (respectively above) which the chiral symmetry is spontaneously broken.

QCD thermodynamics at Nt = 8 and 12

We present results from studies of high temperature QCD with two flavors of Kogut-Susskind quarks on 16 3 × 8 lattices at a quark mass of am q = 0.00625 and on 24 3 × 12 lattices at quark masses am q = 0.008 and 0.016. The value of the crossover temperature is consistent with that obtained on coarser lattices and/or at larger quark masses. Results are presented for the chiral order parameter and for the baryon number susceptibility.

Evidence for meson clouds around hadrons in full lattice QCD

We investigate chiral symmetry breaking locally around a static quark in the framework of lattice QCD by calculating the correlation of the Polyakov loop with the chiral order parameter. We observe a restoration of chiral symmetry in the vicinity of the color source with a different mechanism in both phases of QCD. In the hadronic phase the chiral condensate is screened by a pion cloud, and the effect is more pronounced for lighter dynamical quarks. Above the deconfinement phase transition we find that the Polyakov loop is surrounded by a cloud of scalar σ-mesons.

Chiral quark dynamics in dense nuclear matter

We consider a new approach to the description of dense nuclear matter in the framework of chirally symmetric, quark-based hadron models. As previously in the Skyrme model, the dense environment is described in terms of hyperspherical cells of unit baryon number. The intrinsic curvature of these cells generates a new gauge interaction for the quark fields which mediates interactions with the ambient matter. We apply this approach to the Nambu-Jona-Lasinio (NJL) model, construct its curved-space quark propagator and solve the ladder Bethe-Salpeter equation for the pion. We find a high-density phase transition to chiral restoration, discuss the density dependence of the chiral order parameter and of the pion properties, and compare with results of the conventional chemical-potential approach. The new approach can additionally describe baryon-density-free cavities in the dense medium.

Exploring lattice quantum chromodynamics by cooling.

The effect of cooling on a number of observables is calculated in SU(2) lattice gauge theory. The static quark-antiquark potential and spin-dependent interactions are studied, and the topological charge is monitored. The chiral symmetry breaking order parameter $\langle \overline{\chi}\chi \rangle$ and meson correlators are calculated using staggered fermions. Interactions on the distance scale of a few lattice spacings are found to be essentially eliminated by cooling, including the spin-dependent potentials. $\langle \overline{\chi}\chi \rangle$ and meson correlators up to time separations of several lattice spacings relax very quickly to their free-field values. At larger times, there is evidence of a difference between the pseudoscalar and vector channels. A fit to the pseudoscalar correlation function yields ``mass'' values about $2/3$ (in lattice units) of the uncooled masses. These results raise the question of how to reconcile the large-time behavior of the hadron correlators with the fact that the spin-dependent potentials and $\langle \overline{\chi}\chi \rangle$ essentially disappear (in lattice units) after only a small amount of cooling.

Susceptibilities, the specific heat, and a cumulant in two-flavor QCD.

We study the quark mass dependence of various response functions, which contribute to chiral susceptibilities and the specific heat in the staggered fermion formulation of two-flavour QCD. This yields information about the critical exponents $\alpha$, $\beta$ and $\delta$. In the case of the chiral susceptibility, obtained as derivative of the chiral order parameter with respect to the quark mass, we calculate all contributions. This allows to construct a cumulant of the order parameter, which is a scaling function and yields a direct determination of the critical exponent $\delta$. All our results are consistent with a second order phase transition.