849 research outputs found
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
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
Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
We present a simple approximation of the non-perturbative renormalization
group designed for the Kardar-Parisi-Zhang equation and show that it yields the
correct phase diagram, including the strong-coupling phase with reasonable
scaling exponent values in physical dimensions. We find indications of a
possible qualitative change of behavior around . We discuss how our
approach can be systematically improved.Comment: 4 pages, 1 figure, references added, minor change
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 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
Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
With a view to study the convergence properties of the derivative expansion
of the exact renormalization group (RG) equation, I explicitly study the
leading and next-to-leading orders of this expansion applied to the
Wilson-Polchinski equation in the case of the -vector model with the
symmetry . As a test, the critical exponents and as well as the subcritical exponent (and higher ones) are estimated
in three dimensions for values of ranging from 1 to 20. I compare the
results with the corresponding estimates obtained in preceding studies or
treatments of other exact RG equations at second order. The
possibility of varying allows to size up the derivative expansion method.
The values obtained from the resummation of high orders of perturbative field
theory are used as standards to illustrate the eventual convergence in each
case. A peculiar attention is drawn on the preservation (or not) of the
reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday.
Final versio
Critical Phenomena in Continuous Dimension
We present a calculation of critical phenomena directly in continuous
dimension d employing an exact renormalization group equation for the effective
average action. For an Ising-type scalar field theory we calculate the critical
exponents nu(d) and eta(d) both from a lowest--order and a complete
first--order derivative expansion of the effective average action. In
particular, this can be used to study critical behavior as a function of
dimensionality at fixed temperature.Comment: 5 pages, 1 figure, PLB version, references adde
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