772 research outputs found
Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order
On the example of the three-dimensional Ising model, we show that
nonperturbative renormalization group equations allow one to obtain very
accurate critical exponents. Implementing the order of the
derivative expansion leads to and to an anomalous dimension
which is significantly improved compared with lower orders
calculations.Comment: 4 pages, 3 figure
Non-perturbative Approach to Critical Dynamics
This paper is devoted to a non-perturbative renormalization group (NPRG)
analysis of Model A, which stands as a paradigm for the study of critical
dynamics. The NPRG formalism has appeared as a valuable theoretical tool to
investigate non-equilibrium critical phenomena, yet the simplest -- and
nontrivial -- models for critical dynamics have never been studied using NPRG
techniques. In this paper we focus on Model A taking this opportunity to
provide a pedagological introduction to NPRG methods for dynamical problems in
statistical physics. The dynamical exponent is computed in and
and is found in close agreement with results from other methods.Comment: 13 page
Reaction-diffusion processes and non-perturbative renormalisation group
This paper is devoted to investigating non-equilibrium phase transitions to
an absorbing state, which are generically encountered in reaction-diffusion
processes. It is a review, based on [Phys. Rev. Lett. 92, 195703; Phys. Rev.
Lett. 92, 255703; Phys. Rev. Lett. 95, 100601], of recent progress in this
field that has been allowed by a non-perturbative renormalisation group
approach. We mainly focus on branching and annihilating random walks and show
that their critical properties strongly rely on non-perturbative features and
that hence the use of a non-perturbative method turns out to be crucial to get
a correct picture of the physics of these models.Comment: 14 pages, submitted to J. Phys. A for the proceedings of the
conference 'Renormalization Group 2005', Helsink
Non perturbative renormalization group and momentum dependence of n-point functions (II)
In a companion paper (hep-th/0512317), we have presented an approximation
scheme to solve the Non Perturbative Renormalization Group equations that
allows the calculation of the -point functions for arbitrary values of the
external momenta. The method was applied in its leading order to the
calculation of the self-energy of the O() model in the critical regime. The
purpose of the present paper is to extend this study to the next-to-leading
order of the approximation scheme. This involves the calculation of the 4-point
function at leading order, where new features arise, related to the occurrence
of exceptional configurations of momenta in the flow equations. These require a
special treatment, inviting us to improve the straightforward iteration scheme
that we originally proposed. The final result for the self-energy at
next-to-leading order exhibits a remarkable improvement as compared to the
leading order calculation. This is demonstrated by the calculation of the shift
, caused by weak interactions, in the temperature of Bose-Einstein
condensation. This quantity depends on the self-energy at all momentum scales
and can be used as a benchmark of the approximation. The improved
next-to-leading order calculation of the self-energy presented in this paper
leads to excellent agreement with lattice data and is within 4% of the exact
large result.Comment: 35 pages, 11 figure
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
Non perturbative renormalisation group and momentum dependence of -point functions (I)
We present an approximation scheme to solve the Non Perturbative
Renormalization Group equations and obtain the full momentum dependence of the
-point functions. It is based on an iterative procedure where, in a first
step, an initial ansatz for the -point functions is constructed by solving
approximate flow equations derived from well motivated approximations. These
approximations exploit the derivative expansion and the decoupling of high
momentum modes. The method is applied to the O() model. In leading order,
the self energy is already accurate both in the perturbative and the scaling
regimes. A stringent test is provided by the calculation of the shift in the transition temperature of the weakly repulsive Bose gas, a quantity
which is particularly sensitive to all momentum scales. The leading order
result is in agreement with lattice calculations, albeit with a theoretical
uncertainty of about 25%.Comment: 48 pages, 15 figures A few minor corrections. A reference adde
Exciton Gas Compression and Metallic Condensation in a Single Semiconductor Quantum Wire
We study the metal-insulator transition in individual self-assembled quantum
wires and report optical evidences of metallic liquid condensation at low
temperatures. Firstly, we observe that the temperature and power dependence of
the single nanowire photoluminescence follow the evolution expected for an
electron-hole liquid in one dimension. Secondly, we find novel spectral
features that suggest that in this situation the expanding liquid condensate
compresses the exciton gas in real space. Finally, we estimate the critical
density and critical temperature of the phase transition diagram at
cm and K, respectively.Comment: 4 pages, 5 figure
Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions
The well-established effective action and effective potential framework from
the quantum field theory domain is adapted and successfully applied to
classical field theories of the Doi and Peliti type for diffusion controlled
reactions. Through a number of benchmark examples, we show that the direct
calculation of the effective potential in fixed space dimension to
one-loop order reduces to a small set of simple elementary functions,
irrespective of the microscopic details of the specific model. Thus the
technique, which allows one to obtain with little additional effort, the
potentials for a wide variety of different models, represents an important
alternative to the standard model dependent diagram-based calculations. The
renormalized effective potential, effective equations of motion and the
associated renormalization group equations are computed in spatial
dimensions for a number of single species field theories of increasing
complexity.Comment: Plain LaTEX2e, 32 pages and three figures. Submitted to Journal of
Statistical Physic
The Competitive Diffusion of Gases in a Nanoporous Zeolite Using a Slice Selection Procedure
The study of the co-diffusion of several gases through a microporous solid and of the resulting
instantaneous distribution (out of equilibrium) of the adsorbed phases is particularly important in
many fields, such as gas separation, heterogeneous catalysis, etc. Classical H NMR imaging is a
good technique for visualizing these processes but, since the signal obtained is not specific for each
gas, each experiment has to be performed several times under identical conditions, and each time
with only one incompletely deuterated gas. In contrast, we have proposed a new NMR imaging
technique (based on the so-called NMR slice selection procedure) which gives a signal
characteristic of each adsorbed gas. It can therefore provide directly, at every moment and at every
level of the crystallite bed, the distribution of several gases competing in diffusion and adsorption.
Solutions to the direct and inverse problems are based on Heaviside’s operational method and
Laplace integral transformation. New procedures for identifying diffusion coefficients for co-
diffusing components (benzene and hexane) in intra- and intercrystallite spaces were implemented,
using high-speed gradient methods and mathematical diffusion models, as well as the NMR spectra
of the adsorbed mass distribution of each component in the zeolite bed. These diffusion coefficients
were obtained as a function of time for different positions along the bed. Benzene and hexane
concentrations in the inter- and intracrystallite spaces were calculated for every position in the bed
and for different adsorption times
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
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