Session J29: Non-Equilibrium Statistical Mechanics

Three-dimensional Potts systems with magnetic friction

Using extensive Monte Carlo simulations we study the properties of the non-equilibrium phase transition encountered in driven three-dimensional Potts systems with magnetic friction. Our system consists of two three-dimensional blocks, coupled through boundary spins, that move along their boundaries with a constant relative velocity. Changing the number of states in the system from two (Ising case) to nine states, we find different scenarios for the surface behavior depending on whether the bulk transition is continuous or discontinuous. In order to fully assess the properties of this non-equilibrium phase transition, we vary systematically the strength of the coupling between the two blocks as well as the value of the relative velocity. For strong couplings between the blocks the phase transition is found to be strongly anisotropic.   

Non-equilibrium steady states in two-temperature Ising models with Kawasaki dynamics

From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. In both one and two dimensions, systems attached to two distinct heat reservoirs exhibit many of the hallmarks of phase transition. When such systems settle into a non-equilibrium steady-state they exhibit numerous interesting phenomena, including an unexpected ``freezing by heating.'' There are striking and surprising similarities between the behavior of these systems in one and two dimensions, but also intriguing differences. These phenomena will be explored and possible approaches to understanding the behavior will be suggested.   

Aging processes in systems with anomalous slow dynamics

Recent studies of coarsening in disordered systems show a crossover from an initial, transient, power-law domain growth to a slower logarithmic growth. Due to the anomalous slow dynamics, numerical simulations are usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. In order to gain some new insights into the non-equilibrium properties of systems with logarithmic growth, we study two simple driven systems, the one-dimensional ABC-model and a related domain model with simplified dynamics, where the asymptotic regime can be accessed. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth.   

Random Fields at a Nonequilibrium Phase Transition

We study nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such random-field disorder is known to have dramatic effects: it prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we show that the phase transition of the one-dimensional generalized contact process persists in the presence of random-field disorder. The ultraslow dynamics in the symmetry-broken phase is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by large-scale Monte Carlo simulations.   

Monte-Carlo simulations of the clean and disordered contact process in three space dimensions

The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte-Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality. This work has been supported in part by the NSF under grants no. DMR-0906566 and DMR-1205803.   

Fluctuation Effects in the Pair Annihilation Process with Levy Dynamics

Reaction diffusion models provide a plethora of intensively studied classical nonequilibrium many body systems. One example is the diffusion limited pair annihilation process $A+A\to 0$, where the reactants diffuse in space and annihilate on contact. Inspired by the fact that many phenomena observed in nature exhibit superdiffusive behavior, we investigate the pair annihilation process in the case where the particles perform superdiffusion, realized by Levy flights. As a consequence, the critical dimension depends continuously on the control parameter of the Levy flight distribution. This instance is used to study the density decay in the pair annihilation process close to the critical dimension by means of the non-perturbative renormalization group theory. Close to the critical dimension, long-range fluctuations cause the law of mass action to break down. One crucial consequence of these fluctuations is that the law of mass action is complemented by additional non-analytic correction terms above the critical dimension. An increasing number of those corrections accumulate and give an essential contribution as the critical dimension is approached.   

Directed polymers in random media with short-range correlated disorder

One-dimensional boundary interfaces between different phases are described at macroscopic scales by a rough fluctuating line, whose geometrical properties are dictated by the disorder in the underlying medium, by the temperature of the environment, and by the elastic properties of the line. A widely used and successful model is the directed polymer in a random medium, pertaining to the Kardar-Parisi-Zhang (KPZ) universality class. Much is known for this continuous model when the disorder is uncorrelated, and it has allowed to understand the static and dynamical features of experimental systems ranging from magnetic interfaces to liquid crystals. We show that short-range correlations in the disorder at a scale $\xi>0$ modify the uncorrelated (i.e. zero $\xi$) picture in a non-obvious way. If the geometrical fluctuations are still described by the celebrated 2/3 KPZ exponent, characteristic amplitudes are however modified even at scales much larger than $\xi$, in a well-controlled and rather universal manner. Our results are also relevant to describe the slow (so called `creep') motion of interfaces in random media, and more formally (trough replicae) one-dimensional gases of bosons interacting with softened delta potential.   

Novel phases in an accelerated exclusion process

We introduce a class of distance-dependent interactions in an accelerated exclusion process (AEP) inspired by the cooperative speed-up observed in transcribing RNA polymerases. In the simplest scenario, each particle hops to the neighboring site if vacant \emph{and} when joining a cluster of particles, triggers the frontmost particle to hop. Through both simulation and theoretical work, we discover that the steady state of AEP displays a discontinuous transition with periodic boundary condition. The system transitions from being homogeneous (with augmented currents) to phase-segregated. More surprisingly, the current-density relation in the phase-segregated state is simply $J=1-\rho$, indicating the particles (or holes) are moving at unit velocity despite the inclusion of long-range interactions.   

Intrinsically Localized Modes in the three-dimensional Quantal Fermi-Pasta-Ulam Lattice

Intrinsically Localized Modes (ILMs) are spatially localized oscillatory modes in homogeneous lattices, that are stabilized by anharmonic interactions. ILMs are frequently found in classical low-dimensional systems, where the frequency of the oscillations is a continuous variable. By contrast, due to the internal frequencies quantized,the quantum systems support a hierarch of excitations. The hierarchy of quantal excitations can be described in terms of a hierarchy of bound states of a multiple numbers of phonons. In one-dimension, the existence of the ILMs is ensured for any strength of the repulsive interactions by the divergent van-Hove singularities in the multi-phonon density of states. Inelastic neutron scattering measurements on NaI have revealed unexpected excitations which have been interpreted in terms of ILMs. Since the energies of the observed excitations are discrete, the experiments indicate that the ILMs have quantum character. Therefore, we search for low-energy quantized ILMs in a three-dimensional generalization of the Fermi-Pasta-Ulam lattice. We find that quantized ILMs may exist for values of the interaction strengths which exceeds a critical value. We examine the polarization-dependence, dispersion and the spatial characteristics of the lowest-energy ILMs.   

Dynamics of Linked and Knotted Vortices

Recently developed experimental methods have allowed us to generate topologically linked fluid vortices for the first time. The intrinsically geometric nature of vortex dynamics allows us to measure physical quantities, such as energy, by reconstructing the core centerline in three-dimensions using high-speed laser scanning tomography. This novel approach offers insights into the evolution of linked and knotted vortices up to and through changes in topology.   

Thermally Activated Avalanches in Twinned Crystals

In previous work it was shown that the power-spectrum of the energy release in a twinned crystal under deformation, exhibits a transition from a low-temperature power-law to a high temperature activated dynamics. In this work we provide a statistical mechanics explanation to this behavior based on the understanding that the origin of the power-law behavior stems from a pattern of vertical twins that forms at the onset of yield, and serves as pinning sites to the motion of the (horizontal) twins. The transition to activated behavior is explained by a master equation based on a ``trap model.''   

Exploring the scaling laws of crystal plasticity with a Phase Field Crystal model

A wealth of experiments and simulations the last years has cemented the fact that crystalline materials deform in an intermittent way with slip-avalanches that are power-law distributed. Recently we showed that zero temperature discrete dislocation dynamics simulations predict mean field scaling exponents for both static and dynamic critical exponents. To model a wider range of experimental observations and predict the dependence on experimental parameters that are not captured by discrete dislocation dynamics we work with a Phase Field Crystal (PFC) model in two dimensions. The PFC model has the advantage that it does not require any ad hoc assumptions about the dislocation interaction or their creation and annihilation. It also models the dislocation dynamics at finite temperature. We extract the avalanche distributions and show that they scale according to the Mean Field Depinning universality class even though there is no quenched disorder.   

Intermittency in brittle cracks: Model experiment in artificial rocks

Continuum theory fails to account for disorder effect on the crack propagation in brittle heterogeneous materials: It can explain neither the crackling dynamics, nor the statistics of the macro-scale mechanical observables. In this context, some tools issued from out-of-equilibrium statistical physics that identifies crack propagation onset with a depinning transition appear promising, but lack for quantitative comparisons with experiments. We designed a model experiment set up based on a material with tunable micro-scale (ceramics of sintered polymer beads) in which tensile cracks is grown over a wide range of speeds. Crack length, mechanical energy and acoustic emission (AE) are monitored with good resolution (ms for the first two, $\mu$s for AE) during the experiments. These measures were used (i) to provide information on the nature of the acoustic energy emitted during a breaking event, (ii) to unravel the relation between material toughness and relative system size. We believe our experiment to find applications in mechanical engineering, by helping to understand the microstructural disorder effect on the toughness properties. In statistical physics, it provides a model system to study collective complex crackling dynamics. Finally, in geophysics it help to interpret AE signal used to monitor the damage in Earth crust.