A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations

We revisit the renormalization of Phi-derivable approximations from a slightly different point of view than the one which is usually followed in previous works. We pay particular attention to the question of the existence of a solution to the self-consistent equation that defines the two-point function in the Cornwall-Jackiw-Tomboulis formalism and to the fact that some of the ultraviolet divergences which appear if one formally expands the solution in powers of the bare coupling do not always appear as divergences at the level of the solution itself. We discuss these issues using a particular truncation of the Phi functional, namely the simplest truncation which brings non-trivial momentum and field dependence to the two-point function.Comment: 30 pages, 12 figure

Renormalization and resummation in finite temperature field theories

Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of counterterms: one is a direct method where the necessary counterterms are constructed order by order; the other is a general one, based on renormalization group arguments. We demonstrate at one hand that, in mass independent schemes, mass resummation can be performed by gap equations renormalized prior to the substitution of the resummed mass for its argument. On the other hand it is shown that any (momentum-independent) form of mass and coupling constant resummation is compatible with renormalization, and one can explicitly construct the corresponding counterterms.Comment: 10 pages, 4 figures, revtex

Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory

We study the phase transition of a real scalar phi^4 theory in the two-loop Phi-derivable approximation using the imaginary time formalism, extending our previous (analytical) discussion of the Hartree approximation. We combine Fast Fourier Transform algorithms and accelerated Matsubara sums in order to achieve a high accuracy. Our results confirm and complete earlier ones obtained in the real time formalism [1] but which were less accurate due to the integration in Minkowski space and the discretization of the spectral density function. We also provide a complete and explicit discussion of the renormalization of the two-loop Phi-derivable approximation at finite temperature, both in the symmetric and in the broken phase, which was already used in the real-time approach, but never published. Our main result is that the two-loop Phi-derivable approximation suffices to cure the problem of the Hartree approximation regarding the order of the transition: the transition is of the second order type, as expected on general grounds. The corresponding critical exponents are, however, of the mean-field type. Using a "RG-improved" version of the approximation, motivated by our renormalization procedure, we find that the exponents are modified. In particular, the exponent delta, which relates the field expectation value phi to an external field h, changes from 3 to 5, getting then closer to its expected value 4.789, obtained from accurate numerical estimates [2].Comment: 54 pages, 16 figure

Classical order parameter dynamics and the decay of a metastable vacuum state

Transition of the ground state of a classical Phi^4 theory in 2+1 dimensions is studied from a metastable state into the stable equilibrium. The transition occurs in the broken Z_2 symmetry phase and is triggered by a vanishingly small amplitude homogeneous external field h. A phenomenological theory is proposed in form of an effective equation of the quantitatively accounts for the decay of the false vacuum. The large amplitude transition of the order parameter between the two minima displays characteristics reflecting dynamical aspects of the Maxwell construction

Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion

A fully explicit renormalized quantum action functional is constructed for the O(N)-model in the auxiliary field formulation at next-to-leading order (NLO) of the 1/N expansion. Counterterms are consistently and explicitly derived for arbitrary constant vacuum expectation value of the scalar and auxiliary fields. The renormalized NLO pion propagator is exact at this order and satisfies Goldstone's theorem. Elimination of the auxiliary field sector at the level of the functional provides with order N^0 accuracy the renormalized effective action of the model in terms of the original variables. Alternative elimination of the pion and sigma propagators provides the renormalized NLO effective potential for the expectation values of the N-vector and of the auxiliary field with the same accuracy.Comment: RevTeX4, 19 pages, 3 figures. Version published Phys. Rev.

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Strange mass dependence of the tricritical point in the U(3)_L x U(3)_R chiral sigma model

We study the strange quark mass dependence of the tricritical point of the U(3)_L x U(3)_R linear sigma model in the chiral limit. Assuming that the tricritical point is at a large strange mass value, the strange sector as well as the \eta-a_0 sector decouples from the light degrees of freedom which determines the thermodynamics. By tracing this decoupling we arrive from the original U(3)_L x U(3)_R symmetric model, going through the U(2)_L x U(2)_R symmetric one, at the SU(2)_L x SU(2)_R linear sigma model. One-loop level beta functions for the running of the parameters in each of these models and tree-level matching of the coupling of these models performed at intermediate scales are used to determine the influence of the heavy sector on the parameters of the SU(2)_L x SU(2)_R linear sigma model. By investigating the thermodynamics of this latter model we identified the tricritical surface of the U(3)_L x U(3)_R linear sigma model in the chiral limit. To apply the results for QCD we used different scenarios for the m_s and \mu_q dependence of the effective model parameters, then the \mu_q^TCP(m_s) function can be determined. Depending on the details, a curve bending upwards or downwards near \mu_q=0 can be obtained, while with explicit chemical potential dependence of the parameters the direction of the curve can change with m_s, too.Comment: 17 pages, 6 figures, uses revtex4-

Human disturbances and predation on artificial ground nests across an urban gradient

Perturbaciones antropogénicas y depredación en nidos artificiales en el suelo en un gradiente urbano En nuestro estudio con nidos artificiales observamos que la ausencia de especies de aves que nidifican en el suelo en el centro urbano y en barrios residenciales se debía a las molestias causadas por personas y animales domésticos (perros y gatos) y no a la depredación. Además, la presión por depredación fue superior en la periferia de la ciudad debido al mayor número de depredadores naturales. Nuestros resultados sugieren que la planificación y creación de zonas protegidas podrían aumentar la posibilidad de que las aves que nidifican en el suelo se establecieran y se reprodujeran en paisajes dominados por los humanos.Perturbaciones antropogénicas y depredación en nidos artificiales en el suelo en un gradiente urbano En nuestro estudio con nidos artificiales observamos que la ausencia de especies de aves que nidifican en el suelo en el centro urbano y en barrios residenciales se debía a las molestias causadas por personas y animales domésticos (perros y gatos) y no a la depredación. Además, la presión por depredación fue superior en la periferia de la ciudad debido al mayor número de depredadores naturales. Nuestros resultados sugieren que la planificación y creación de zonas protegidas podrían aumentar la posibilidad de que las aves que nidifican en el suelo se establecieran y se reprodujeran en paisajes dominados por los humanos.In our study with artificial nests we observed that the absence of ground nesting bird species in the city centre and in residential districts was due to disturbance by humans and domestic animals (dogs and cats) rather than to predation. Furthermore, predation pressure was higher in the outskirts of the city due to the greater number of natural predators. Our results suggest that planning and creating undisturbed areas could increase the chances of ground nesting birds settling and breeding in human–dominated landscapes

Extending structures I: the level of groups

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A general product, which we call the unified product, is constructed such that both the crossed product and the bicrossed product of two groups are special cases of it. It is associated to $H$ and to a system $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$ called a group extending structure and we denote it by $H \ltimes S$. There exists a group structure on $E$ containing $H$ as a subgroup if and only if there exists an isomorphism of groups $(E, \cdot) \cong H \ltimes S$, for some group extending structure $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$. All such group structures on $E$ are classified up to an isomorphism of groups that stabilizes $H$ by a cohomological type set ${\mathcal K}^{2}_{\ltimes} (H, (S, 1_S))$. A Schreier type theorem is proved and an explicit example is given: it classifies up to an isomorphism that stabilizes $H$ all groups that contain $H$ as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor

Predation of common wall lizards: experiences from a study using scentless plasticine lizards

The potential influence of predators on lacertid lizards has been studied by using models made of plasticine which shows the attack marks of predators and as such allows their identification and estimation of predation pressure. The general aim was to study predation on plasticine models of lizards and to improve methods, since the results depend on the number of plasticine models used, their spatial pattern and the duration of experiments. We estimated the density of the common wall lizard Podarcis muralis population on stone walls of a vineyard in the city of Pécs (Hungary) in August 2015 in order to imitate the real density in our experiment with plasticine models. The density of common wall lizards was 8.2 ind. /100 m2 and accordingly we placed 25 scentless plasticine lizards on the stone walls on the first transect with 10 m distance between them, which imitates the real pattern. In the second transect 25 lizard models were placed more sparsely, the distance between them being 20 m. During four weeks the predation rate was 24% in densely spaced plasticine lizards and 40% in sparsely spaced plasticine lizards, but the difference was not significant. The daily survival rate of densely spaced lizards was 0.99 (=99.1%) and that of sparsely spaced lizard models was 0.98 (=98.25%), but this difference was not significant either. On the basis of marks left on plasticine lizards, mammal predators (e.g. beech marten) dominated, while the impact of bird predators was smaller than expected. Predators attacked the head of plasticine lizards more frequently than their trunk, tail or limbs, but a significant preference of body parts was not detected. From our experience it is important to study the distribution and density of real animals, to imitate their real pattern, instead of an arbitrarily designed experiment with models. The typical scent of plasticine also could influence the results, which can be avoided by using scentless plasticine models coated with liquid rubber. We suggest the calculation of daily survival rates in order to produce results that allow the comparison of different studies