Léonie Canet

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

Nonperturbative renormalization group for the Kardar-Parisi-Zhang equation.

\partial^2

Nonperturbative Renormalization-Group Study of Reaction-Diffusion Processes

of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents

Nonperturbative renormalization group for the Kardar-Parisi-Zhang equation: general framework and first applications.

\nu

General framework of the non-perturbative renormalization group for non-equilibrium steady states

and

Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions

\eta

Quantitative phase diagrams of branching and annihilating random walks

. 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.

Optimization of field-dependent nonperturbative renormalization group flows

We present a simple approximation of the nonperturbative 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 d=4. We discuss how our approach can be systematically improved.

What can be learnt from the nonperturbative renormalization group

We generalize nonperturbative renormalization group methods to nonequilibrium critical phenomena. Within this formalism, reaction-diffusion processes are described by a scale-dependent effective action, the flow of which is derived. We investigate branching and annihilating random walks with an odd number of offspring. Along with recovering their universal physics (described by the directed percolation universality class), we determine their phase diagrams and predict that a transition occurs even in three dimensions, contrarily to what perturbation theory suggests.

A non-perturbative approach to critical dynamics

We present an analytical method, rooted in the nonperturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one. We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones. We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling function. We find a very satisfactory quantitative agreement with the exact result from Prähofer and Spohn [J. Stat. Phys. 115, 255 (2004)]. In particular, we obtain for the universal amplitude ratio g_{0}≃1.149(18), to be compared with the exact value g_{0}=1.1504... (the Baik and Rain [J. Stat. Phys. 100, 523 (2000)] constant). We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and its symmetries, without further assumptions on the existence of scaling or on the form of the scaling function.