123 research outputs found
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 debÃa 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 podrÃan 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 debÃa 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 podrÃan 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 be a group and a set such that . We shall describe
and classify up to an isomorphism of groups that stabilizes the set of all
group structures that can be defined on such that is a subgroup of .
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 and to a system called a group extending
structure and we denote it by . There exists a group structure on
containing as a subgroup if and only if there exists an isomorphism of
groups , for some group extending structure
. All such
group structures on are classified up to an isomorphism of groups that
stabilizes by a cohomological type set . A Schreier type theorem is proved and an explicit example is given: it
classifies up to an isomorphism that stabilizes all groups that contain
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
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