Effective lagrangian analysis of the chiral phase transition at finite density

Introducing a finite chemical potential μ for the quark number density ψ^°ψ, we study analytically the restoration of Π^° chiral symmetry as μ is varied. In the strong coupling limit, the effective lagrangian for SU(N) gauge theories coupled to fermion fields in d dimensions is derived for all N. In the case of SU(2) we predict a second order chiral symmetry restoration phase transition, whereas for all N?3 the transition is first order. Predictions are given for the critical values of the chemical potential μ.     

The deconfining phase transition in the finite temperature twisted Eguchi-Kawai model

We present the results obtained from a Monte Carlo study of a finite temperature twisted Eguchi-Kawai model as previously introduced by the authors. The deconfining temperature of the model is determined to be (206 ± 20) Λ_L.     

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     

Deconfining and chiral phase transitions in quantum chromodynamics at finite temperature

We give further arguments to support the claim of Svetitsky and Yaffe that the finite-temperature transition in 4-dimensional SU(N) gauge theories is in the universality class of 3-dimensional Z_N spin models. We show that this implies a smoothing out of the transition when quarks are added to the system as long as N ≠ 3. For N = 3 the pure gauge transition is expected to be first order and will be smoothed by quarks only if the quark contribution to the internal energy is larger than the latent heat of transition.     

Instantons and the chiral phase transition

We examine the role of instantons in the zero-temperature chiral phase transition in an SU(N) gauge theory. For a range of N_f (the number of fermion flavors) depending on N, the theory exhibits an infrared fixed point at coupling _*. As N_f decreases, _* increases, and it eventually exceeds a critical value sufficient to trigger chiral symmetry breaking. For the case N = 2, we estimate the critical values of N_f and _* due to instantons by numerically solving a gap equation with an instanton-generated kernel. We find instanton effects of strength comparable to that of gluon exchange.     

Electromagnetic properties of ice near the water-ice phase transition temperature

Freshwater ice in a cavity was studied under heating to 0°C followed by cooling at a frequency of 6.3 GHz. Splitting of a resonant transmission line at 60–70 MHz was detected. This effect may be associated with the existence of two vibrational modes in ice, with the coupling between them increasing near 0°C. In such a medium, two waves with identical polarizations and similar wavenumbers can exist. This assumption was confirmed experimentally by measuring the 13-GHz radiation transmission through a natural freshwater ice cover. These measurements detected signal oscillations caused by the interference of two waves, with alternation of maxima and minima with a period of 4.6 m, which corresponds to a beat frequency of ～37 MHz.     

Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

The frustrated spin-1/2 J_1a–J_1b–J₂ antiferromagnet with anisotropy on the two-dimensional square lattice was investigated, where the parameters J_1aand J_1b represent the nearest neighbor exchanges and along the x and y directions, respectively. J₂ represents the next-nearest neighbor exchange. The anisotropy includes the spatial and exchange anisotropies. Using the double-time Green’s function method, the effects of the interplay of exchanges and anisotropy on the possible phase transition of the Néel state and stripe state were discussed. Our results indicated that, in the case of anisotropic parameter 0≤η<1, the Néel and stripe states can exist and have the same critical temperature as long as J₂ = J_1b/2. Under such parameters, a first-order phase transformation between the Néel and stripe states can occur below the critical point. For J₂ ≠J_1b/2, our results indicate that the Néel and stripe states can also exist, while their critical temperatures differ. When J₂>J_1b/2, a first-order phase transformation between the two states may also occur. However, for J₂<J_1b/2, the Néel state is always more stable than the stripe state.     

Finite volume effects on the QCD chiral phase transition in the finite size de-pendent Nambu-Jona-Lasinio model

The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.     

Infrared chiral anomaly at finite temperature

We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature T and is present not only in the two point function, but also in all even point amplitudes.     

The chiral phase transition in QCD

The Chiral Phase Transition in QCD is studied analytically by looking at truncations of the Schwinger-Dyson equation for the quark self-mass. We find that the usual implementation of the gluon propagator at non-zero temperature is far too simple. When the gluons are given the correct qualitative non-zero temperature behaviour, the calculation of the critical temperature changes significantly.     

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.     

Mean-field approximation for the chiral soliton in a chiral phase transition

Using the mean-field approximation, we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after chiral restoration. We find that the system has soliton solutions even after chiral restoration, and that they are very different from those before chiral restoration, which indicates that the quarks are still bound after chiral restoration.