632 research outputs found
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
Single-site approximation for reaction-diffusion processes
We consider the branching and annihilating random walk and with reaction rates and , respectively, and hopping rate
, and study the phase diagram in the plane. According
to standard mean-field theory, this system is in an active state for all
, and perturbative renormalization suggests that this mean-field
result is valid for ; however, nonperturbative renormalization predicts
that for all there is a phase transition line to an absorbing state in the
plane. We show here that a simple single-site
approximation reproduces with minimal effort the nonperturbative phase diagram
both qualitatively and quantitatively for all dimensions . We expect the
approach to be useful for other reaction-diffusion processes involving
absorbing state transitions.Comment: 15 pages, 2 figures, published versio
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
General framework of the non-perturbative renormalization group for non-equilibrium steady states
This paper is devoted to presenting in detail the non-perturbative
renormalization group (NPRG) formalism to investigate out-of-equilibrium
systems and critical dynamics in statistical physics. The general NPRG
framework for studying non-equilibrium steady states in stochastic models is
expounded and fundamental technicalities are stressed, mainly regarding the
role of causality and of Ito's discretization. We analyze the consequences of
Ito's prescription in the NPRG framework and eventually provide an adequate
regularization to encode them automatically. Besides, we show how to build a
supersymmetric NPRG formalism with emphasis on time-reversal symmetric
problems, whose supersymmetric structure allows for a particularly simple
implementation of NPRG in which causality issues are transparent. We illustrate
the two approaches on the example of Model A within the derivative expansion
approximation at order two, and check that they yield identical results.Comment: 28 pages, 1 figure, minor corrections prior to publicatio
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
Non-Perturbative Renormalization Group for Simple Fluids
We present a new non perturbative renormalization group for classical simple
fluids. The theory is built in the Grand Canonical ensemble and in the
framework of two equivalent scalar field theories as well. The exact mapping
between the three renormalization flows is established rigorously. In the Grand
Canonical ensemble the theory may be seen as an extension of the Hierarchical
Reference Theory (L. Reatto and A. Parola, \textit{Adv. Phys.}, \textbf{44},
211 (1995)) but however does not suffer from its shortcomings at subcritical
temperatures. In the framework of a new canonical field theory of liquid state
developed in that aim our construction identifies with the effective average
action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich,
\textit{Phys. Rep.}, \textbf{363} (2002))
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
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
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