131 research outputs found
Fixed points and infrared completion of quantum gravity
The phase diagram of four-dimensional EinsteinâHilbert gravity is studied using WilsonÊŒs renormalization group. Smooth trajectories connecting the ultraviolet fixed point at short distances with attractive infrared fixed points at long distances are derived from the non-perturbative graviton propagator. Implications for the asymptotic safety conjecture and further results are discussed
Optimization of field-dependent nonperturbative renormalization group flows
We investigate the influence of the momentum cutoff function on the
field-dependent nonperturbative renormalization group flows for the
three-dimensional Ising model, up to the second order of the derivative
expansion. We show that, even when dealing with the full functional dependence
of the renormalization functions, the accuracy of the critical exponents can be
simply optimized, through the principle of minimal sensitivity, which yields
and .Comment: 4 pages, 3 figure
Superfluidity within Exact Renormalisation Group approach
The application of the exact renormalisation group to a many-fermion system
with a short-range attractive force is studied. We assume a simple ansatz for
the effective action with effective bosons, describing pairing effects and
derive a set of approximate flow equations for the effective coupling including
boson and fermionic fluctuations.
The phase transition to a phase with broken symmetry is found at a critical
value of the running scale. The mean-field results are recovered if boson-loop
effects are omitted. The calculations with two different forms of the regulator
was shown to lead to similar results.Comment: 17 pages, 3 figures, to appear in the proceedings of Renormalization
Group 2005 (RG 2005), Helsinki, Finland, 30 Aug - 3 Sep 200
Non-Perturbative Renormalization Group calculation of the scalar self-energy
We present the first numerical application of a method that we have recently
proposed to solve the Non Perturbative Renormalization Group equations and
obtain the n-point functions for arbitrary external momenta. This method leads
to flow equations for the n-point functions which are also differential
equations with respect to a constant background field. This makes them, a
priori, difficult to solve. However, we demonstrate in this paper that, within
a simple approximation which turns out to be quite accurate, the solution of
these flow equations is not more complicated than that of the flow equations
obtained in the derivative expansion. Thus, with a numerical effort comparable
to that involved in the derivative expansion, we can get the full momentum
dependence of the n-point functions. The method is applied, in its leading
order, to the calculation of the self-energy in a 3-dimensional scalar field
theory, at criticality. Accurate results are obtained over the entire range of
momenta.Comment: 29 page
Infrared fixed point in quantum Einstein gravity
We performed the renormalization group analysis of the quantum Einstein
gravity in the deep infrared regime for different types of extensions of the
model. It is shown that an attractive infrared point exists in the broken
symmetric phase of the model. It is also shown that due to the Gaussian fixed
point the IR critical exponent of the correlation length is 1/2. However,
there exists a certain extension of the model which gives finite correlation
length in the broken symmetric phase. It typically appears in case of models
possessing a first order phase transitions as is demonstrated on the example of
the scalar field theory with a Coleman-Weinberg potential.Comment: 9 pages, 7 figures, final version, to appear in JHE
Non Perturbative Renormalization Group, momentum dependence of -point functions and the transition temperature of the weakly interacting Bose gas
We propose a new approximation scheme to solve the Non Perturbative
Renormalization Group equations and obtain the full momentum dependence of
-point functions. This scheme involves an iteration procedure built on an
extension of the Local Potential Approximation commonly used within the Non
Perturbative Renormalization Group. Perturbative and scaling regimes are
accurately reproduced. The method is applied to the calculation of the shift
in the transition temperature of the weakly repulsive Bose gas, a
quantity which is very sensitive to all momenta intermediate between these two
regions. The leading order result is in agreement with lattice calculations,
albeit with a theoretical uncertainty of about 25%. The next-to-leading order
differs by about 10% from the best accepted result
On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
We study the nature of the confinement phase transition in d=3+1 dimensions
in various non-abelian gauge theories with the approach put forward in [1]. We
compute an order-parameter potential associated with the Polyakov loop from the
knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and
Sp(2) we find a first-order phase transition in agreement with general
expectations. Moreover our study suggests that the phase transition in E(7)
Yang-Mills theory also is of first order. We find that it is weaker than for
SU(N). We show that this can be understood in terms of the eigenvalue
distribution of the order parameter potential close to the phase transition.Comment: 15 page
Optimization of the derivative expansion in the nonperturbative renormalization group
We study the optimization of nonperturbative renormalization group equations
truncated both in fields and derivatives. On the example of the Ising model in
three dimensions, we show that the Principle of Minimal Sensitivity can be
unambiguously implemented at order of the derivative expansion.
This approach allows us to select optimized cut-off functions and to improve
the accuracy of the critical exponents and . The convergence of the
field expansion is also analyzed. We show in particular that its optimization
does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio
Renormalization Flow of Bound States
A renormalization group flow equation with a scale-dependent transformation
of field variables gives a unified description of fundamental and composite
degrees of freedom. In the context of the effective average action, we study
the renormalization flow of scalar bound states which are formed out of
fundamental fermions. We use the gauged Nambu--Jona-Lasinio model at weak gauge
coupling as an example. Thereby, the notions of bound state or fundamental
particle become scale dependent, being classified by the fixed-point structure
of the flow of effective couplings.Comment: 25 pages, 3 figures, v2: minor corrections, version to appear in PR
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