Symmetry Restoring Phase Transition Research Articles

Role of the conserved charges in the chiral symmetry restoration phase transition

The effect of conserved baryon, isospin and strangeness charges on the behavior of phase transitions in dense matter is studied. Baryonic matter is described within the three-flavor Polyakov$-$Nambu$-$Jona-Lasinio model and several charge fractions $Y_Q$ are considered. The role of the vector interaction, which can be important to describe dense systems, is discussed. Special attention is given to the case with charge fraction $Y_Q=0.4$, due to its importance in heavy-ion collisions and core-collapse supernova matter. It is shown that the possible formation of chiral-symmetric quark matter in the laboratory will be favored in asymmetric matter. Besides, the inclusion of the vector interaction reinforces the formation of quark matter at lower densities.

Development of shashlik electromagnetic calorimeter for the NICA/MPD

The main goal of the NICA heavy-ion program at JINR is an experimental investigation into the properties of nuclear matter within the energy region of the maximum baryonic density. The Multi Purpose Detector (MPD) is one of the detectors at NICA collider, which is optimized for the study on properties of hot and dense matter in heavy-ion collisions and, in particular, the search for a manifestation of possible deconfinement and/or chiral symmetry restoration phase transitions, critical end-point and mixed quark-hadron phase. Electromagnetic calorimeter (ECal) is an important part of MPD . The particular goal of MPD-ECal is to measure position and energy of photons and electrons. Taking all factors (high energy resolution, high segmentation, large enough distance to the vertex, small Moliere radius, high magnetic field and high time resolution) into consideration, a shashlik-type electromagnetic calorimeter is selected. Therefore the tower consists of 220 layers of lead plates and scintillator plates whose thicknesses are namely 0.3mm/1.5mm. The tower cell is 4×4 cm2 in size. To reduce the dead zones effect, all towers should be cut from four sides at small angles, which will significantly improve the position resolution and the performance homogeneity of the ECal. Currently, energy deposition, energy resolution and position reconstruction are studied through Monte Carlo simulations. A prototype of shashlik Ecal has been built and the cosmic test results show that the number of photoelectrons (Npe) is around 522. By comparing with the previous ECal experimental results and simulation results, it is indirectly considered that the energy resolution of the prototype has reached 5%/√E (GeV) . Key technologies to increase light yield are being studied and will be used in the development of new prototypes.

Evidence of the QCD Tricritical Endpoint Existence at NICA-FAIR Energies

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Chiral and deconfinement phase transitions in QED3 with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m a on chiral symmetry restoration and deconfinement phase transitions in QED3 are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N c f decreases as the gauge boson mass m a increases, which implies that there exists a boundary that separates the N c f –m a plane into chiral symmetry breaking/confinement region for (N c f , m a ) below the boundary and chiral symmetry restoration/deconfinement region for (N c f , m a ) above it.

Standard model cross-over on the lattice

With the physical Higgs mass the Standard Model symmetry restoration phase transition is a smooth cross-over. We study the thermodynamics of the cross-over using numerical lattice Monte Carlo simulations of an effective SU(2) X U(1) gauge + Higgs theory, significantly improving on previously published results. We measure the Higgs field expectation value, thermodynamic quantities like pressure, energy density, speed of sound and heat capacity, and screening masses associated with the Higgs and Z fields. While the cross-over is smooth, it is very well defined with a width of only approximately 5 GeV. We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result $T_c = 159.5 \pm 1.5$ GeV. Outside of the narrow cross-over region the perturbative results agree well with non-perturbative ones.

Role of strangeness in hybrid stars and possible observables

We study the effects of strangeness on the quark sector of a hybrid star equation of state. Since the model we use to describe quarks is the same as the one we use to describe hadrons, we can also study the effects of strangeness on the chiral symmetry restoration and deconfinement phase transitions (first order or crossover). Finally, we analyze combined effects of hyperons and quarks on global properties of hybrid stars, like mass, radius and cooling profiles. It is found that a large amount of strangeness in the core is related to the generation of twin-star solutions, which can have the same mass as the lower or zero strangeness counterpart, but with smaller radii.

Zero mode in a strongly coupled quark gluon plasma

In connection with massless two-flavor QCD, we analyze the chiral symmetry restoring phase transition using three distinct gluon-quark vertices and two different assumptions about the long-range part of the quark-quark interaction. In each case, we solve the gap equation, locate the transition temperature ${T}_{c}$, and use the maximum entropy method to extract the dressed-quark spectral function at $T>{T}_{c}$. Our best estimate for the chiral transition temperature is ${T}_{c}=147\ifmmode\pm\else\textpm\fi{}8\text{ }\text{ }\mathrm{MeV}$, and the deconfinement transition is coincident. For temperatures markedly above ${T}_{c}$, we find a spectral density that is consistent with those produced using a hard thermal loop expansion, exhibiting both a normal and plasmino mode. On a domain $T\ensuremath{\in}[{T}_{c},{T}_{s}]$, with ${T}_{s}\ensuremath{\simeq}1.5{T}_{c}$, however, with each of the six kernels we considered, the spectral function contains a significant additional feature. Namely, it displays a third peak, associated with a zero mode, which is essentially nonperturbative in origin and dominates the spectral function at $T={T}_{c}$. We suggest that the existence of this mode is a signal for the formation of a strongly coupled quark-gluon plasma and that this strongly interacting state of matter is likely a distinctive feature of the QCD phase transition.

Effective potential and Goldstone bosons in de Sitter space

We investigate nonperturbative infrared effects for the $O(N)$ linear sigma model in de Sitter space using the two-particle irreducible effective action at the Hartree truncation level. This approximation resums the infinite series of so-called superdaisy diagrams. For the proper treatment of ultraviolet divergences, we first study the renormalization of this approximation on a general curved background. Then, we calculate radiatively corrected masses and the effective potential. As a result, spontaneous symmetry breaking is possible; on the other hand, the Goldstone modes acquire a positive definite mass term due to the screening effects of interaction. Possible infrared divergence is self-regulated by the mass term. Furthermore, there is a symmetry-restoring phase transition as a function of the Hubble parameter. In our approximation, the phase transition is of first order.

Universal frozen spectra after time-dependent symmetry restoring phase transitions

For a general O(N) model, we study the time-dependent phase transition from a state with broken symmetry to the symmetric phase . During this non-equilibrium process, the primordial quantum (or thermal) fluctuations of the initial Goldstone modes are frozen and result in a deviation from the final ground (or thermal) state. For very slow transitions, we find that these fluctuations display a universal scaling behaviour. Their spectra are universal functions of a single parameter, which combines the initial frequency of the Goldstone modes and the sweep rate. As a result, the final two-point function is not exponentially suppressed at large distances Δr = r − r′ (as it would be in the ground state) but decays polynomially in 1/|Δr|. Finally, we exemplify this universal behaviour for the transition from the super-fluid phase to the Mott state in the Bose–Hubbard model.

Temperature dependence of the effective bag constant and the radius of a nucleon in the global color symmetry model of QCD

We study the temperature dependence of the effective bag constant, the mass, and the radius of a nucleon in the formalism of the simple global color symmetry model in the Dyson-Schwinger equation approach of QCD with a Gaussian-type effective gluon propagator. We obtain that, as the temperature is lower than a critical value, the effective bag constant and the mass decrease and the radius increases with the temperature increasing. As the critical temperature is reached, the effective bag constant and the mass vanish and the radius tends to infinity. At the same time, the chiral quark condensate disappears. These phenomena indicate that the deconfinement and the chiral symmetry restoration phase transitions can take place at high temperature. The dependence of the critical temperature on the interaction strength parameter in the effective gluon propagator of the approach is given.

Influence of strong magnetic fields and instantons on the phase structure of the two-flavor Nambu–Jona-Lasinio model

Both in heavy-ion collisions as in magnetars very strong magnetic fields are produced, which has its influence on the phases of matter involved. In this paper we investigate the effect of strong magnetic fields (B = 5 m_pi^2 /e = 1.7 x 10^19 G) on the chiral symmetry restoring phase transition using the Nambu-Jona-Lasinio model. It is observed that the pattern of phase transitions depends on the relative magnitude of the magnetic field and the instanton interaction strength. We study two specific regimes in the phase diagram, high chemical potential and zero temperature and vice versa, which are of relevance for neutron stars and heavy-ion collisions respectively. In order to shed light on the behavior of the phase transitions we study the dependence of the minima of the effective potential on the occupation of Landau levels. We observe a near-degeneracy of multiple minima with differing occupation numbers, of which some become the global minimum upon changing the magnetic field or the chemical potential. These minima differ considerably in the amount of chiral symmetry breaking and in some cases also of isospin breaking.

One-loop results for kink and domain wall profiles at zero and finite temperature

Using dimensional regularization, we compute the one-loop quantum and thermal corrections to the profile of the bosonic ($1+1$)-dimensional ${\ensuremath{\varphi}}^{4}$ kink, the sine-Gordon kink, and the $C{P}^{1}$ kink, and higher-dimensional ${\ensuremath{\varphi}}^{4}$ kink domain walls. Starting from the Heisenberg field equation in the presence of the nontrivial kink background we derive analytically results for the temperature-dependent mean field which display the onset of the melting of kinks as the system is heated towards a symmetry-restoring phase transition. The result is shown to simplify significantly when expressed in terms of a self-consistently defined thermal screening mass. In the case of domain walls, we find infrared singularities in the kink profile, which corresponds to interface roughening depending on the system size. Finally we calculate the energy density profile of ${\ensuremath{\varphi}}^{4}$ kink domain walls and find that in contrast to the total surface tension the local distribution requires composite operator renormalization in $3+1$ dimensions.

Anomalously high capacitance of β-rhombohedral boron induced by structural defects

Capacitance and dielectric loss tangent measurements have been carried out for β-rhombohedral boron within the frequency range 102 – 104 Hz and temperature interval 77 – 373 K. Different specimens were studied: high-purity macrocrystals, vapor-liquid-grown faceted crystals, zone-melted single crystals, and crucible-melted polycrystals. Within the whole ranges of measurements, the capacitance of all samples was 10–60 times larger than their geometric capacitance. Temperature dependences of the capacitance reveal two-level step-like behavior. Location of levels is independent from the applied electric field frequency, but at higher frequencies, the capacitance steps shift to lower temperatures. For all frequencies, an abrupt rise in capacitance takes place at one and same temperature ∼ 290 K. At low temperature, dielectric losses are negligible, but they increase towards the room temperature. At ∼ 290 K (i.e., simultaneously with the abrupt rise in capacitance) their value abruptly falls down. Dielectric properties of β-rhombohedral boron are discussed on the basis of generalized barrier model of the heterogeneous semiconductor within its three-layer version. Planar defects like twins and stacking faults characteristic for real crystals are assumed to produce local elastic stresses sufficient for the local lowering in conductivity due to the piezoresistive effect. Consequently, layers adjacent to the planar defects should represent low-conducting inclusions in the relatively high-conducting matrix. In addition, the lesser-conducting barrier layers should appear at their boundaries. Effect at ∼ 290 K seems to be related with a symmetry-restoring phase transition driven by the occupation patterns of certain atomic sites in β-rhombohedral crystalline boron lattice.

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Densityin a Two-Flavor Nambu–Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitionsat zero temperature and finite chemical potentials under electricalneutrality condition has been conducted in a Nambu–Jona-Lasiniomodel to describe two-flavor normal quark matter. Depending on whetherm0/Λ, the ratio of dynamical quark mass in vacuum and the 3Dmomentum cutoff in the loop integrals, is less or greater than 0.413,the phase transition will be of the second or first order.A complete phase diagram of u quark chemical potential versus m0is given. With the electrical neutrality constraint, the region wherethe second order phase transition happens will be wider than the onewithout electrical neutrality limitation. The results also show that,for the value of m0/Λ from QCD phenomenology,the phase transition must be of the first order.

Critical flavor number in the three dimensional Thirring model

We present results of a Monte Carlo simulation of the three dimensional Thirring model with the number of fermion flavors ${N}_{f}$ varied between 2 and 18. By identifying the lattice coupling at which the chiral condensate peaks, simulations are performed at couplings ${g}^{2}({N}_{f})$ corresponding to the strong coupling limit of the continuum theory. The chiral symmetry restoring phase transition is studied as ${N}_{f}$ is increased, and the critical number of flavors estimated as ${N}_{fc}=6.6(1)$. The critical exponents measured at the transition do not agree with self-consistent solutions of the Schwinger-Dyson equations; in particular, there is no evidence for the transition being of infinite order. Implications for the critical flavor number in ${\mathrm{QED}}_{3}$ are briefly discussed.

Polyakov loop in chiral quark models at finite temperature

We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponentially small with the pion mass. To illustrate the point we compute some low energy observables at finite temperature and show that the finite temperature corrections to the low energy coefficients are $N_c$ suppressed due to color average of the Polyakov loop. Our analysis also shows how the phenomenology of chiral quark models at finite temperature can be made compatible with the expectations of chiral perturbation theory. The implications for the simultaneous center symmetry breaking-chiral symmetry restoration phase transition are also discussed.

Hydrodynamics of Sakai–Sugimoto model in the quenched approximation

Abstract We study transport properties of the finite temperature Sakai–Sugimoto model. The model represents a holographic dual to ( 4 + 1 ) -dimensional supersymmetric SU ( N c ) gauge theory compactified on a circle with anti-periodic boundary conditions for fermions, coupled to N f left-handed quarks and N f right-handed quarks localized at different points on the compact circle. We analytically compute the speed of sound and the sound wave attenuation in the quenched approximation. Since confinement/deconfinement (and the chiral symmetry restoration) phase transitions are first order in this model, we do not see any signature of these phase transitions in the transport properties.

Self-consistent calculations of spectral densities in the [formula omitted] model: improving the Hartree–Fock approximation by including nonzero decay widths

We study the linear sigma model with O ( N ) symmetry at nonzero temperature in the framework of the Cornwall–Jackiw–Tomboulis formalism. Extending the set of two-particle irreducible diagrams by adding sunset diagrams to the usual Hartree–Fock contributions, we derive a new approximation scheme which extends the standard Hartree–Fock approximation by the inclusion of nonzero decay widths. In this approximation, in-medium modifications of the meson masses as well as decay and collisional broadening effects are self-consistently taken into account. As compared to the standard Hartree–Fock approximation, the temperature for the chiral symmetry restoring phase transition is lowered by ∼ 20 – 25 % . For large temperatures, the spectral densities of the σ-meson and the pion become degenerate, as required for the chirally symmetric phase.

Lattice study of anisotropic quantum electrodynamics in three dimensions

We present results from a Monte Carlo simulation of noncompact lattice QED in three dimensions on a ${16}^{3}$ lattice in which an explicit anisotropy between $x$ and $y$ hopping terms has been introduced into the action. This formulation is inspired by recent formulations of anisotropic ${\mathrm{QED}}_{3}$ as an effective theory of the non-superconducting portion of the cuprate phase diagram, with relativistic fermion degrees of freedom defined near the nodes of the gap function on the Fermi surface, the anisotropy encapsulating the different Fermi and Gap velocities at the node, and the massless photon degrees of freedom reproducing the dynamics of the phase disorder of the superconducting order parameter. Using a parameter set corresponding in the isotropic limit to broken chiral symmetry (in field theory language) or a spin density wave (in condensed matter physics language), our results show that the renormalized anisotropy, defined in terms of the ratio of correlation lengths of gauge invariant bound states in the $x$ and $y$ directions, exceeds the explicit anisotropy $\ensuremath{\kappa}$ introduced in the lattice action, implying in contrast to recent analytic results that anisotropy is a relevant deformation of ${\mathrm{QED}}_{3}$. There also appears to be a chiral symmetry restoring phase transition at ${\ensuremath{\kappa}}_{c}\ensuremath{\simeq}4.5$, implying that the pseudogap phase persists down to $T=0$ in the cuprate phase diagram.

Transition in the spectrum of the topological sector ofϕ24theory at strong coupling

We investigate the strong coupling region of the topological sector of the two-dimensional $\phi^4$ theory. Using discrete light cone quantization (DLCQ), we extract the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluate the expectation value of the integral of the normal ordered $\phi^2$ operator and we extract the number density of constituents in these states. A coherent state variational calculation confirms that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation is extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrate that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extract the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpret the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional $\phi^4$ theory.