Chiral Symmetry Restoration at Finite Temperature in the Linear Sigma--Model

The temperature behaviour of meson condensates $$and$$ is calculated in the $SU(3)\times SU(3)$-linear sigma model. The couplings of the Lagrangian are fitted to the physical $\pi,K,\eta,\eta'$ masses, the pion decay constant and a $O^+(I=0)$ scalar mass of $m_\sigma=1.5$ GeV. The quartic terms of the mesonic interaction are converted to a quadratic term with the help of a Hubbard-Stratonovich transformation. Effective mass terms are generated this way, which are treated self-consistently to leading order of a $1/N$-expansion. We calculate the light $$ and strange $<\bar s s>$-quark condensates using PCAC relations between the meson masses and condensates. For a cut-off value of 1.5 GeV we find a first-order chiral transition at a critical temperature $T_c\sim 161$ MeV. At this temperature the spontaneously broken subgroup $SU(2)\times SU(2)$ is restored. Entropy density, energy density and pressure are calculated for temperatures up to and slightly above the critical temperature. To our surprise we find some indications for a reduced contribution from strange mesons for $T\geq T_c$.Comment: 17 pages, HD--TVP--93--15. (3 figures - available on request

Pair-factorized steady states on arbitrary graphs

Stochastic mass transport models are usually described by specifying hopping rates of particles between sites of a given lattice, and the goal is to predict the existence and properties of the steady state. Here we ask the reverse question: given a stationary state that factorizes over links (pairs of sites) of an arbitrary connected graph, what are possible hopping rates that converge to this state? We define a class of hopping functions which lead to the same steady state and guarantee current conservation but may differ by the induced current strength. For the special case of anisotropic hopping in two dimensions we discuss some aspects of the phase structure. We also show how this case can be traced back to an effective zero-range process in one dimension which is solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur

Mass condensation on networks

We construct classical stochastic mass transport processes for stationary states which are chosen to factorize over pairs of sites of an undirected, connected, but otherwise arbitrary graph. For the special topology of a ring we derive static properties such as the critical point of the transition between the liquid and the condensed phase, the shape of the condensate and its scaling with the system size. It turns out that the shape is not universal, but determined by the interplay of local and ultralocal interactions. In two dimensions the effect of anisotropic interactions of hopping rates can be treated analytically, since the partition function allows a dimensional reduction to an effective one-dimensional zero-range process. Here we predict the onset, shape and scaling of the condensate on a square lattice. We indicate further extensions in the outlook

Implementierung eines verlustleistungsoptimierten Dezimators für kaskadierte Sigma-Delta Analog-Digital Umsetzer

Dieser Beitrag stellt die Implementierung eines neuartigen Ansatzes einer effizienten Dezimator-Architektur für kaskadierte Sigma-Delta Modulatoren vor. Die Rekombinationslogik kaskadierter Modulatoren und die Korrektur des Verstärkungsfehlers zeitkontinuierlicher (CT) Modulatoren werden in die erste Stufe des Dezimators integriert. Eine entsprechende Filtertopologie wird hergeleitet und auf einem Hardware-Emulator der Firma Mentor Graphics implementiert. Der Vergleich der vorgeschlagenen Struktur mit einer herkömmlichen Implementierung zeigt eine nennenswerte Verbesserung der Effizienz

QCD and the Chiral Critical Point

As an extension of $QCD$, consider a theory with ``$2+1$'' flavors, where the current quark masses are held in a fixed ratio as the overall scale of the quark masses is varied. At nonzero temperature and baryon density it is expected that in the chiral limit the chiral phase transition is of first order. Increasing the quark mass from zero, the chiral transition becomes more weakly first order, and can end in a chiral critical point. We show that the only massless field at the chiral critical point is a sigma meson, with the universality class that of the Ising model. Present day lattice simulations indicate that $QCD$ is (relatively) near to the chiral critical point.Comment: 7 pages + 2 figures, BNL-GGP-

Critical Phenomena with Linked Cluster Expansions in a Finite Volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish 1st from 2nd order transitions within a finite size scaling analysis. The criterion applies also to other methods for investigating the phase structure such as Monte Carlo simulations. Our computational tools are illustrated at the example of scalar O(N) models with four and six-point couplings for $N=1$ and $N=4$ in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.Comment: 36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and tarred tex file hdth9607.te

Influence of the U(1)_A Anomaly on the QCD Phase Transition

The SU(3)_{r} \times SU(3)_{\ell} linear sigma model is used to study the chiral symmetry restoring phase transition of QCD at nonzero temperature. The line of second order phase transitions separating the first order and smooth crossover regions is located in the plane of the strange and nonstrange quark masses. It is found that if the U(1)_{A} symmetry is explicitly broken by the U(1)_{A} anomaly then there is a smooth crossover to the chirally symmetric phase for physical values of the quark masses. If the U(1)_{A} anomaly is absent, then there is a phase transition provided that the \sigma meson mass is at least 600 MeV. In both cases, the region of first order phase transitions in the quark mass plane is enlarged as the mass of the \sigma meson is increased.Comment: 5 pages, 3 figures, Revtex, discussion extended and references added. To appear in PR

Dynamics of Phase Transitions: The 3D 3-state Potts model

In studies of the QCD deconfining phase transition or cross-over by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. In this paper we extend our previous study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model, which serves as an effective model for some QCD properties. We investigate the linear theory of spinodal decomposition in some detail. It describes the early time evolution of the 3D model under a quench from the disordered into the ordered phase well, but fails in 2D. Further, the quench leads to competing vacuum domains, which are difficult to equilibrate, even in the presence of a small external magnetic field. From our hysteresis study we find, as before, a dynamics dominated by spinodal decomposition. There is evidence that some effects survive in the case of a cross-over. But the infinite volume extrapolation is difficult to control, even with lattices as large as $120^3$.Comment: 12 pages; added references, corrected typo

Tuning the shape of the condensate in spontaneous symmetry breaking

We investigate what determines the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional grid and interacting if they are at the same or at neighboring nodes. We predict the envelope of the condensate and the scaling of its width with the system size for various interaction potentials and show how to tune the shape from a delta-peak to a rectangular or a parabolic-like form.Comment: 4 pages, 2 figures, major revision, the title has been change