Chiral phase transition at high temperature and density in the QCD-like theory

The chiral phase transition at finite temperature T and/or chemical potential $\mu$ is studied using the QCD-like theory with a variational approach. The ``QCD-like theory'' means the improved ladder approximation with an infrared cutoff in terms of a modified running coupling. The form of Cornwall-Jackiw-Tomboulis effective potential is modified by the use of the Schwinger-Dyson equation for generally nonzero current quark mass. We then calculate the effective potential at finite T and/or $\mu$ and investigate the phase structure in the chiral limit. We have a second-order phase transition at $T_c=129$ MeV for $\mu=0$ and a first-order one at $\mu_c=422$ MeV for T=0. A tricritical point in the T-$\mu$ plane is found at T=107 MeV, $\mu=210$ MeV. The position is close to that of the random matrix model and some version of the Nambu-Jona-Lasinio model.Comment: 10 pages, 6 figures. Accepted for publication in Physical Review

Constituent quark model for nuclear stopping in high energy nuclear collisions

We study the nuclear stopping in high energy nuclear collisions using the constituent quark model. It is assumed that wounded nucleons with different number of interacted quarks hadronize in different ways. The probabilities of having such wounded nucleons are evaluated for proton-proton, proton-nucleus and nucleus-nucleus collisions. After examining our model in proton-proton and proton-nucleus collisions and fixing the hadronization functions, it is extended to nucleus-nucleus collisions. It is used to calculate the rapidity distribution and the rapidity shift of final state protons in nucleus-nucleus collisions. The computed results are in good agreement with the experimental data on ^{32}\mbox{S} +\ ^{32}\mbox{S} at $E_{lab} = 200$ AGeV and ^{208}\mbox{Pb} +\ ^{208}\mbox{Pb} at $E_{lab} = 160$ AGeV. Theoretical predictions are also given for proton rapidity distribution in ^{197}\mbox{Au} +\ ^{197}\mbox{Au} at $\sqrt{s} = 200$ AGeV (BNL-RHIC). We predict that the nearly baryon free region will appear in the midrapidity region and the rapidity shift is $\langle \Delta y \rangle = 2.22$.Comment: 40 pages, 16 Postscript figures, submitted to Phys. Rev.

Detection of weak-order phase transitions in ferromagnets by ac resistometry

It is shown that ac resistometry can serve as an effective tool for the detection of phase transitions, such as spin reorientation or premartensitic phase transitions, which generally are not disclosed by dc resistivity measurement. Measurement of temperature dependence of impedance, $Z(T)$, allows one to unmask the anomaly, corresponding to a weak-order phase transition. The appearance of such an anomaly is accounted for by a change in the effective permeability $\mu$ of a sample upon the phase transition. Moreover, frequency dependence of $\mu$ makes it possible to use the frequency of the applied ac current as an adjusting parameter in order to make this anomaly more pronounced. The applicability of this method is tested for the rare earth Gd and Heusler alloy Ni$_2$MnGa.Comment: 4 pages, 2 figures, to be published in J. Appl. Phys., v.94(5

Projection Operator Approach to Langevin Equations in ϕ4\phi^4 Theory

We apply the projection operator method (POM) to $\phi^4$ theory and derive both quantum and semiclassical equations of motion for the soft modes. These equations have no time-convolution integral term, in sharp contrast with other well-known results obtained using the influence functional method (IFM) and the closed time path method (CTP). However, except for the fluctuation force field terms, these equations are similar to the corresponding equations obtained using IFM with the linear harmonic approximation, which was introduced to remove the time-convolution integral. The quantum equation of motion in POM can be regarded as a kind of quantum Langevin equation in which the fluctuation force field is given in terms of the operators of the hard modes. These operators are then replaced with c-numbers using a certain procedure to obtain a semiclassical Langevin equation. It is pointed out that there are significant differences between the fluctuation force fields introduced in this paper and those introduced in IFM. The arbitrariness of the definition of the fluctuation force field in IFM is also discussed.Comment: 35pages,2figures, Prog. Theor. Phys. Vol. 107 No. 5 in pres

Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde