21 research outputs found
Quantitative Phase Diagrams of Branching and Annihilating Random Walks
We demonstrate the full power of nonperturbative renormalisation group
methods for nonequilibrium situations by calculating the quantitative phase
diagrams of simple branching and annihilating random walks and checking these
results against careful numerical simulations. Specifically, we show, for the
2A->0, A -> 2A case, that an absorbing phase transition exists in dimensions
d=1 to 6, and argue that mean field theory is restored not in d=3, as suggested
by previous analyses, but only in the limit d -> .Comment: 4 pages, 3 figures, published version (some typos corrected
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
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
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
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
Far-from-equilibrium quantum many-body dynamics
The theory of real-time quantum many-body dynamics as put forward in Ref.
[arXiv:0710.4627] is evaluated in detail. The formulation is based on a
generating functional of correlation functions where the Keldysh contour is
closed at a given time. Extending the Keldysh contour from this time to a later
time leads to a dynamic flow of the generating functional. This flow describes
the dynamics of the system and has an explicit causal structure. In the present
work it is evaluated within a vertex expansion of the effective action leading
to time evolution equations for Green functions. These equations are applicable
for strongly interacting systems as well as for studying the late-time
behaviour of nonequilibrium time evolution. For the specific case of a bosonic
N-component phi^4 theory with contact interactions an s-channel truncation is
identified to yield equations identical to those derived from the 2PI effective
action in next-to-leading order of a 1/N expansion. The presented approach
allows to directly obtain non-perturbative dynamic equations beyond the widely
used 2PI approximations.Comment: 20 pp., 6 figs; submitted version with added references and typos
corrected
Phase Structure and Compactness
In order to study the influence of compactness on low-energy properties, we
compare the phase structures of the compact and non-compact two-dimensional
multi-frequency sine-Gordon models. It is shown that the high-energy scaling of
the compact and non-compact models coincides, but their low-energy behaviors
differ. The critical frequency at which the sine-Gordon model
undergoes a topological phase transition is found to be unaffected by the
compactness of the field since it is determined by high-energy scaling laws.
However, the compact two-frequency sine-Gordon model has first and second order
phase transitions determined by the low-energy scaling: we show that these are
absent in the non-compact model.Comment: 21 pages, 5 figures, minor changes, final version, accepted for
publication in JHE
Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
We study the occurrence of spontaneous symmetry breaking (SSB) for O (N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N = 1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions
What can be learnt from the nonperturbative renormalization group?
We point out some limits of the perturbative renormalization group used in
statistical mechanics both at and out of equilibrium. We argue that the non
perturbative renormalization group formalism is a promising candidate to
overcome some of them. We present some results recently obtained in the
literature that substantiate our claims. We finally list some open issues for
which this formalism could be useful and also review some of its drawbacks.Comment: 9 pages, 1 figur
What can be learnt from the nonperturbative renormalization group?
9 pages, 1 figureInternational audienceWe point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of them. We present some results recently obtained in the literature that substantiate our claims. We finally list some open issues for which this formalism could be useful and also review some of its drawbacks