Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models.
Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.
Functional renormalization group and the field theory of disordered elastic systems.
- P. Le Doussal, K. Wiese, P. Chauve
- PhysicsPhysical review. E, Statistical, nonlinear, and…
- 27 April 2003
This work examines several routes out of this dilemma, which lead to a unique renormalizable field theory at two-loop order, and clarifies the dependence of universal amplitudes on the boundary conditions at large scale.
Renormalization of pinned elastic systems: how does it work beyond one loop?
The field theories for pinned elastic systems at equilibrium and at depinning are studied and it is proved that two-loop renormalizability is proved and that random field attracts shorter range disorder.
Driven particle in a random landscape: disorder correlator, avalanche distribution, and extreme value statistics of records.
The renormalized force correlator Delta(micro) can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder, and the Middleton theorem is violated.
Size distributions of shocks and static avalanches from the functional renormalization group.
This work studies static avalanches, or shocks, defined here as jumps between distinct global minima upon changing an external field, and shows how the full statistics of these jumps is encoded in the functional-renormalization-group fixed-point functions to obtain the size distribution P(S) ofstatic avalanches in an expansion in the internal dimension d of the interface.
Random walkers in one-dimensional random environments: exact renormalization group analysis.
- P. Le Doussal, C. Monthus, D. Fisher
- Physics, MathematicsPhysical review. E, Statistical physics, plasmas…
- 20 November 1998
Sinai's model of diffusion in one dimension with random local bias is studied by a real space renormalization group, which yields exact results at long times and rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are characterized in detail.
Freezing of dynamical exponents in low dimensional random media.
A particle in a random potential with logarithmic correlations in dimensions d = 1,2 is shown to undergo a dynamical transition at T(dyn)>0, and anomalous scaling occurs in the creep dynamics, relevant to dislocation motion experiments.
Winding of planar Gaussian processes
We consider a smooth, rotationally invariant, centered Gaussian process in the plane, with arbitrary correlation matrix Ctt′. We study the winding angle ϕt, around its center. We obtain a closed…
Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions.
This work provides the first exact calculation of the height distribution at arbitrary time t of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions and obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian.
Height fluctuations of a contact line: A direct measurement of the renormalized disorder correlator
We measure the center-of-mass fluctuations of the height of a contact line at depinning for two different systems: liquid hydrogen on a rough cesium substrate and isopropanol on a silicon wafer…