Fázisátalakulások és szimmetriasértő fázisok dinamikája = Dynamics of phase transitions and symmetry breaking phases

Az SU(3)_LxSU(3)_R szimmetriájú lineáris szigma modell egy-hurok színtű optimalizált perturbációszámításbeli megoldásával meghatároztuk a pion-kaon tömegsík elsőrendű királis fázisátalakulási tartományának másodrendű határvonalát és megbecsültük az m_pi=0 tengelyen levő trikritikus pont helyét. A modell csatolási állandóit a tömegsík kiterjedt tartományában elfolytattunk a királis perturbációszámítás segítségével. A SU(3)_LxSU(3)_R szimmetriájú királis kvark modellben megállapítottuk, hogy a tömegsík--mu_B térbeli másodrendű fázisátalakulások felülete monoton módon a crossover tartományban levő fizikai pont felé hajlik a mu_B barion kémiai potenciál növelésével. Ennek megfelelően, a tömegek fizikai értékeire létezik a mu_B-T síkon egy kritikus végpont (CEP), ahol mu_B növelésével a fázisátalakulás crossover típusból elsőrendűre vált át. Meghatároztuk a CEP kritikus tartományának alakját, a kritikus exponens értékét, valamint az izospin és ritka kémiai potenciálok hatását a CEP helyére. Az ellentagok explicit meghatározását lehetővé tevő módszert dolgoztunk ki a különböző globális szimmetriával rendelkező kvantumtérelméletek kétrészecske irreducibilis (2PI) közelítésben származtatott funkcionálegyenleteinek nem-perturbatív renormálására. A Standard Modell Higgs szektorát nem megfigyelhető fantom terekkel egészítve ki a nagy-N közelítés vezető rendjében adódó renormalizált egyenletek numerikus megoldásával példát mutattunk a dinamikai szimmetriasértés megvalósulására. | In the SU(3)_LxSU(3)_R linear sigma model the 2nd order boundary between the crossover and 1st order chiral phase transition regions of the m_pi-m_K-plane was determined with the one-loop optimised perturbation theory and the location of the tricritical point on the m_pi=0 axis estimated. In a wide domain of the mass-plane the parameters of the model were determined using the chiral perturbation theory. In the SU(3)_LxSU(3)_R chiral quark model the surface of 2nd order transition points in the m_pi-m_K-mu_B space was found to bend with increasing baryon chemical potential mu_B towards the physical point located in the crossover region of the m_pi-m_K mass plane. For physical m_pi and m_K this behaviour implies the existence in mu_B-T plane of the critical end point CEP where the transition turns with increasing mu_B from crossover into 1st order type. The shape of the critical region around the CEP and the effect of the isospin and hypercharge chemical potentials on CEP's location were determined. A method was developed to explicitly determine the counterterms which renormalises the functional equations obtained in the two-particle irreducible (2PI) approximation to quantum field theories with various global symmetries. Extending the Higgs sector of the Standard Model with unobservable phantom fields the possibility of dynamical symmetry breaking was demonstrated by solving numerically the renormalised equations obtained in the leading order of the large-N approximation

The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N=1 and N=4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Phi-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Phi-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.Comment: 26 pages, 15 figures, uses RevTeX4-1, published versio

Loss of solution in the symmetry improved Phi-derivable expansion scheme

We consider the two-loop Phi-derivable approximation for the O(2)-symmetric scalar model, augmented by the symmetry improvement introduced in [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)], which enforces Goldstone's theorem in the broken phase. Although the corresponding equations admit a solution in the presence of a large enough infrared (IR) regulating scale, we argue that, for smooth ultraviolet (UV) regulators, the solution is lost when the IR scale becomes small enough. Infrared regular solutions exist for certain non-analytic UV regulators, but we argue that these solutions are artifacts which should disappear when the sensitivity to the UV regulator is removed by a renormalization procedure. The loss of solution is observed both at zero and at finite temperature, although it is simpler to identify in the latter case. We also comment on possible ways to cure this problem.Comment: 20 pages, 7 figures, uses elsarticle, published versio

Thermodynamics and phase transition of the O(N) model from the two-loop Phi-derivable approximation

We discuss the thermodynamics of the O(N) model across the corresponding phase transition using the two-loop Phi-derivable approximation of the effective potential and compare our results to those obtained in the literature within the Hartree-Fock approximation. In particular, we find that in the chiral limit the transition is of the second order, whereas it was found to be of the first order in the Hartree-Fock case. These features are manifest at the level of the thermodynamical observables. We also compute the thermal sigma and pion masses from the curvature of the effective potential. In the chiral limit, this guarantees that the Goldstone's theorem is obeyed in the broken phase. A realistic parametrization of the model in the N=4 case, based on the vacuum values of the curvature masses, shows that a sigma mass of around 450 MeV can be obtained. The equations are renormalized after extending our previous results for the N=1 case by means of the general procedure described in [J. Berges et al., Annals Phys. 320, 344-398 (2005)]. When restricted to the Hartree-Fock approximation, our approach reveals that certain problems raised in the literature concerning the renormalization are completely lifted. Finally, we introduce a new type of Phi-derivable approximation in which the gap equation is not solved at the same level of accuracy as the accuracy at which the potential is computed. We discuss the consistency and applicability of these types of "hybrid" approximations and illustrate them in the two-loop case by showing that the corresponding effective potential is renormalizable and that the transition remains of the second order.Comment: 26 pages, 9 figures, uses RevTeX4-1, published versio

Existence of the critical endpoint in the vector meson extended linear sigma model

The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential mu_B within an extended (2+1) flavor Polyakov constituent quark-meson model which incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a chi^2-minimization procedure which selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners' masses and of the mixing angles for the pseudoscalar eta-eta' and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the T-mu_B phase diagram of the model and find that a critical end point exists for parameters of the model, which give acceptable values of chi^2.Comment: 21 pages, 8 color eps figures, published versio

Chiral phase transition in the vector meson extended linear sigma model

In the framework of an SU(3) (axial)vector meson extended linear sigma model with additional constituent quarks and Polyakov loops, we investigate the effects of (axial)vector mesons on the chiral phase transition. The parameters of the Lagrangian are set at zero temperature and we use a hybrid approach where in the effective potential the constituent quarks are treated at one-loop level and all the mesons at tree-level. We have four order parameters, two scalar condensates and two Polyakov loop variables and their temperature and baryochemical potential dependence are determined from the corresponding field equations. We also investigate the changes of the tree-level scalar meson masses in the hot and dense medium.Comment: 5 pages, 6 figure

Pad\'e approximants and analytic continuation of Euclidean Phi-derivable approximations

We investigate the Pad\'e approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second Riemann sheet. We test this method using various benchmarks at zero temperature: a simple perturbative approximation as well as the two-loop Phi-derivable approximation. The analytic continuation method is then applied to Euclidean data previously obtained in the O(4) symmetric model (within a given renormalization scheme) to assess the difference between zero-momentum and pole masses, which is in general a difficult question to answer within nonperturbative approaches such as the Phi-derivable expansion scheme.Comment: 20 pages, 8 figures, uses RevTeX 4-

O(4) ϕ^4 model as an effective light meson theory: A lattice-continuum comparison

We investigate the possibility of using the 4 dimensional $O(4)$ symmetric $\phi^4$ model as an effective theory for the sigma-pion system. We carry out lattice Monte Carlo simulations to establish the triviality bound in the case of explicitly broken symmetry and to compare it with results from continuum functional methods. In case of a physical parametrization we find that triviality restricts the possible lattice spacings to a narrow range, therefore cutoff independence in the effective theory sense is practically impossible for thermal quantities. We match the critical line in the space of bare couplings in the different approaches and compare vacuum physical quantities along the line of constant physics (LCP).Comment: 9 pages, 8 figures, published versio

Néhány palackozott romániai ásványvíz jellemzése a teljes ásványi anyag tartalom alapján: Characterization of some bottled Romanian mineral waters on the basis of the total mineral content

Romania has many mineral water sources due to its geological features. In the present study, bottles of 26 Romanian mineral water brands were obtained from the market to make a characterization based on the pH, conductivity, and fixed residue content. According to the total fixed residue, the distribution of low, medium, and highly mineralized water was 43.9%, 41.46%, and 14.63%, respectively. The mean of fixed residue concentration was 763.3 mg/L, ranging from 40.37 mg/L to 2603 mg/L. The pH values of the still mineral waters varied between 6.86 and 7.91, while the pH values of the sparkling mineral waters were the lowest (4.7). The conductivity was strongly related to the concentration of the ions, therefore the maximum measured conductivity for the still waters was 573 µS/cm, for the partially sparkling waters 2133 µS/cm, and for the sparkling mineral waters 3079 µS/cm.  Kivonat Románia geológiai adottságainak köszönhetően sok ásványvízforrással rendelkezik. Jelen kutatás során 26 romániai palackozott ásványvizet elemeztünk, a pH, a vezetőképesség és a rögzített maradéktartalom alapján. A teljes fix maradékra összpontosítva az alacsony, közepes és erősen mineralizált víz eloszlása ​​43,9%, 41,46% és 14,63% volt. A rögzített átlagos maradéktartalom 763,3 mg/l volt, ugyanakkor 40,37 mg/l és 2603 mg/l között változott. Az szénsavmentes ásványvizek pH-értékei 6,86 és 7,91 között változtak, míg a szénsavval dúsított ásványvizek pH-értékei a legalacsonyabbak (4,7). A vezetőképesség szorosan összefügg az ionok koncentrációjával, így a szénsavmentes ásványvizek maximális mért vezetőképessége 573 µS/cm, a részben szénsavas vizeknél 2133 µS/cm, a szénsavas ásványvizek esetében pedig a vezetőképesség 3079 µS/cm volt.&nbsp

Scale dependence of the Kondo interaction in the functional renormalization group formalism

Scale evolution of interactions between a Weyl fermion and a heavy magnetic impurity is calculated non-perturbatively using the functional renormalization group technique. Using an expansion around the vanishing pairing gap, we derive the flow equations for all possible quartic couplings in the system. We find that contrary to conventional perturbation theory, the usual spin-spin isotropic interaction necessarily splits into two invariant parts during the scale evolution, which are fully allowed by the $SU(2)$ spin-rotation symmetry. We also find the existence of an infrared stable interacting fixed point, which can be responsible for intermediate-coupling screening effects. The calculation scheme presented here is rather general and expected to be easily applicable to various spin-spin-like interactions in fermionic systems.Comment: 12 pages, 4 figures, matches published versio