# Groupe de Physique Statistique

## Equipe 106, Institut Jean Lamour

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## mercredi 26 mai 2004 - vendredi 28 mai 2004

#### Programme de l'atelier

mercredi 26 mai 2004
14:00 - Kurt Binder
15:00 - Jorg Baschnagel
15:30 - Ralph Kenna
15:45 - Eric Brunet
17:00 - Simon Trebst
17:45 - Fabien Alet
jeudi 27 mai 2004
09:00 - H. Singer
09:45 - Florent Krzakala
11:00 - Attila Rakos
11:45 - Cécile Appert
14:00 - Des Johnston
14:45 - Ferenc Iglói
15:30 - Gregor Diezemann
16:45 - Jaroslav Ilnytskyi
vendredi 28 mai 2004
09:00 - Gunter Schütz
09:45 - Yurij Holovatch
11:00 - Michel Pleimling
11:45 - Wolfhard Janke
14:45 - Frédéric van Wijland

#### Orateurs

Fabien Alet
Superfluid - Insulator transition in 2D: A cluster Monte Carlo study
In this talk, I will present results on the pure and disorder Bosonic Hubbard model in 2D at zero temperature, obtained with a new worm cluster algorithm.
Cécile Appert
Asymmetric simple exclusion process and road traffic
After a brief overview of recent results obtained with large deviation functions in the ASEP model, I will focus on a phenomenological approach which allows to study the system also in non-stationary states. A variant of the ASEP with metastability will then be discussed. I will conclude by mentioning how cellular automata can be used for road traffic.
Jorg Baschnagel
Molecular dynamics simulations on the glassy behavior of polymer melts
We present results from molecular-dynamics simulations for a bead-spring model of a polymer melt . We explore the correlation between the structure and the dynamics as the melt is cooled towards its glass transition. We show that two time regimes can be distinguished in the supercooled state: an intermediate time regime in which the amorphous packing between the monomers determines the structural relaxation of the melt, and a late time regime where the relaxation is dominated by chain-connectivity.
Kurt Binder
Monte Carlo simulations of glass transition in thin films
Molecular Dynamics studies of simple models (short non-entangled polymer chains and a binary Lennard-Jones mixture) of glassing fluids confined between various types of walls are discussed, with an emphasis on the understanding of the nature of the glass transition from the analysis of confinement effects. Particularly attention is paid to the possible conclusions on a characteristic length that grows, as the glass transition is approached. Particulary useful is the analysis for the local relaxation time $\tau(z)$, $z$ being the distance from the closest confining wall. Both smooth and rough walls are considered (the latter are constructed such that there is almost no layering effect). In all cases it is found that the characteristic lengths do increase with decreasing temperature, albeit rather slowly; the relevance of these lengths for the slowing down near the glass transition remains doubtful.
Eric Brunet
Directed polymers in random media: exact cumulants for the free energy and winding number
Using the replica trick and the Bethe Ansatz, we have calculated for a finite geometry the first cumulants of the free energy and the winding number around an obstacle of a directed polymer in a random medium.
Gregor Diezemann
Fluctuation-disspiation relations and master equations
The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation with continuous time. It is shown that in general the linear response cannot be expressed via time-derivatives of the correlation function alone, but an additional function $\xi(t,t_w)$, which has been rarely discussed before is required. This function depends on the two times also relevant for the response and the correlation and vanishes under equilibrium conditions. $\xi(t,t_w)$ can be expressed in terms of the propagators and the transition rates of the master equation but it is not related to any physical observable in an obvious way. Instead, it is determined by inhomogeneities in the temporal evolution of the distribution function of the stochastic variable under consideration. $\xi(t,t_w)$ is considered for some examples of stochastic models, in particular for an extremely simple kinetic random energy model. Even in this case $\xi(t,t_w)$ does not vanish. However, it can be related to the 'aging part' of the two-time correlation function. This fact is of importance in the discussion of out-of-equlibrium extensions of the FDT.
Yurij Holovatch
Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster
In this talk I discuss the influence of quenched disorder on the scaling properties of long flexible polymer chains (modeled as self-avoiding walks, SAWs). The examples include: scaling of a SAW at presence of a weak uncorrelated or long-range correlated disorder; scaling of a SAW on percolation cluster.
Ferenc Iglói
Asymmetric simple exclusion process with quenched disorder
We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the average distance traveled by a particle, $x$, scales with the time, $t$, as $x \sim t^{1/z}$, with a dynamical exponent $z > 1$. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method we analytically calculate, $z_{pr}$, for particlewise (pt) disorder, which is argued to be related to the dynamical exponent for sitewise (st) disorder as $z_{st}=z_{pr}/2$. In the symmetric situation with zero mean drift the particle diffusion is ultra-slow, logarithmic in time.
Jaroslav Ilnytskyi
The relaxation processes in a bulk system of dendritic molecules
We consider the internal dynamics of branched macromolecules in a melt via molecular dynamics simulation. The study is motivated by our previous simulations of a single liquid crystalline dendrimer in a solvent and some attempts to simulate the corresponding bulk phases. Two models are considered - the first is of generation one dendrimers with long tails (topologically rather similar to a star-like polymer) and the second one of generation three dendrimers with shorter tails. Both types of dendritic molecules are of real-life carbosilane type and the AMBER force field is used to describe the intramolecular interactions. We study the intramolecular dynamics for different densities and temperatures and observe different regimes, including reptation-like behaviour. The simulations are compared partly with the results of Rouse-Zimm theory. Another practical issue is to select the relevant types of intramolecular moves which is vital for developing an effective Monte Carlo algorithms for given systems.
Wolfhard Janke
Folding Lattice Proteins
We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast PERM (Pruned-Enriched Rosenbluth Method) chain-growth algorithm with multicanonical reweighting strategies for sampling the full energy space. Since the density of states contains all energetic information of a statistical system, we can directly calculate the mean energy, specific heat, Helmholtz free energy, and entropy for all temperatures. We demonstrate the efficiency of this new method in applications to lattice proteins described by the effective hydrophobic-polar HP model. For a selected sample of HP sequences we first discuss ground-state properties, and then identify and characterize the transitions between native, globule, and random coil states as temperature increases. For short chains with up to 19 monomers our numerical results are validated by comparison with recently obtained exact enumeration data.
Des Johnston
A grand canonical ASEP
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for nonequilibrium dynamics, in particular driven diffusive processes. It is usually considered in a canonical ensemble in which the number of sites is fixed. We observe that the grand-canonical normalizations for the ASEP with both random sequential and parallel updates are remarkably simple and clearly show the correspondence with various two dimensional path problems.
Ralph Kenna
Scaling at higher-order phase transitions
Florent Krzakala
Out-of-equilibrium Kawasaki dynamics of Ferromagnetic models
The dynamics of ferromagnetic system of Ising spins evolving under Kawasaki constraints is a classical coarsenning problem. I will review recent results for two-time correlation and response functions both at criticality and in the ferromagnetic phase, stressing the difference and similarities between Kawasaki and Glauber dynamics for response, correlation, and fluctuation-dissipation properties.
Michel Pleimling
Out-of-equilibrium critical dynamics at surfaces
Nonequilibrium surface autocorrelation and autoresponse functions are studied in semi-infinite critical systems. In the short time regime an unusual stationary stretched exponential behaviour of the dynamical surface autocorrelation is observed in cases where the equilibrium surface autocorrelation function decays very fast. This behaviour, which is due to a novel mechanism called cluster dissolution, also takes place in the critical semi-infinite three-dimensional Ising model. Ageing processes showing up in the dynamical scaling regime are also discussed. Integrated surface response functions are confronted with predictions coming from the theory of local scale invariance. The asymptotic value of the nonequilibrium surface fluctuation-dissipation ratio is shown to depend on the value of the surface scaling dimension.
Why spontaneous symmetry breaking disappear in a bridge system with PDE-friendly boundaries
We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system.
Attila Rakos
Bethe Ansatz and Random Matrices
Recently for many growth models of the KLS universality class the distribution of the height was calculated and it was shown that for late times this relates to the Tracy-Widom distribution of the largest eigenvalues of some Gaussian random matrix ensembles. In the present work we study how this result relates to the Bethe Ansatz solution of a class of asymmetric exclusion processes.
Gunter Schütz
Phase coexistence in nonequilibrium reaction-diffusion systems: Exact results
We study the flow of fluctuations in driven diffusive systems with two conserved densities. This yields a criterion for the microscopic stability of shocks. We also investigate the hydrodynamic limit on the Euler scale and obtain two coupled nonlinear PDE's for the evolution of the local density. For the selection of the physical solution of this system of conservation laws we introduce a viscosity matrix. Simulation of a specific lattice model suggests that, unlike in one-component systems, the choice of the infinitesimal viscosity term is not irrelevant in finite systems. This raises the unexpected question how the physical viscosity term has to be determined. For a special class of systems we propose a prescription that reproduces Monte-Carlo data reasonably well.
H. Singer
Analysis of scale-invariant properties in experimentally grown morphologies of diffusion limited growth in 3 dimensions
We investigate in our in situ experiments three-dimensional xenon crystals during free growth into pure supercooled melt. Supercooling is the only control parameter of the system and determines the morphology of the crystal. Dendritic, seaweed and doublon morphologies have been observed. Characteristic parameters of dendrites and doublons were deduced from experimental data and compared with theoretical predictions and simulations of 2D and 3D phase field models. We present a morphology diagram based on our simulations and our experimental results. Fractal dimensions (contour and area) have been determined by correlation method and an optimized box-counting algorithm. We present a technique to detect integral hidden length scales in experimental structures and find these length scales to depend on morphology. We present a method of reconstructing the three-dimensional shape of an experimentally grown xenon dendrite based on a hybrid approach of sophisticated image processing and measured parameters of dendrites. The reconstruction is quantitative and reveals more details as conventional techniques. A quantitative investigation of the dendrite surface and volume shows in both cases a power law dependence on distance from the tip and temporal evolution. Three-dimensional doublons are studied experimentally and are reconstructed. A hyperbolic dependence of the width of the growth channel on supercooling is found. The temporal evolution of doublons and the relaxtion to dendritic growth is analyzed and quantitatively reconstructed.
Simon Trebst
Overcoming entropic barriers in disordered spin systems
We present an adaptive algorithm which overcomes the slowdown of flat-histogram sampling by optimizing the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. We discuss applications to classical spin lattice systems.
Frédéric van Wijland
Current-carrying ground-state of a quantum system: the Ising chain in a transverse field
The nonequilibrium properties of the ground-state of the quantum Ising chain in a transverse field are considered: correlation functions and distribution of global observables exhibit features quite distinct from their equilibrium counterparts