arXiv subjects

Hugues Chaté

Publications and source records attributed to Hugues Chaté.

87 records · Page 5Linked to original sources

arXiv2005

Langevin description of critical phenomena with two symmetric absorbing states

On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical integration in physical dimensions. Our findings fully account for and clarify the intricate picture known so far from the aggregation of partial results obtained with microscopic models. We argue that the direct transition from disorder to one of two absorbing states is best described as a (generalized) voter critical point and show that it can be split into an Ising and a directed percolation transitions in dimensions larger than one.

cond-mat.stat-mech↗

arXiv2004

From ballistic to Brownian vortex motion in complex oscillatory media

We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDL) is accompanied by an intrinsic drift of the pattern. Single vortex motion changes from ballistic flights at a well-defined angle from the SDL to Brownian-like diffusion when the turbulent character of the medium increases. It gives rise, in non-turbulent multi-spiral regimes, to a novel ``vortex liquid''.

nlin.PS↗

arXiv2004

Noise-induced macroscopic bifurcations in globally-coupled chaotic units

Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.

cond-mat.stat-mech↗

arXiv2003

Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models

We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm the recent proposal that, at critical points, the large-time ``fluctuation-dissipation ratio'' $X_\infty$ is a universal amplitude ratio and find in particular $X_\infty \approx 0.33(2)$ and $X_\infty = 1/2$ for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.

cond-mat.stat-mech↗

arXiv2003

Absorbing Phase Transitions with Coupling to a Static Field and a Conservation Law

The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions give rise to a new universality class distinct from that characterizing the depinning of the so-called linear interface model.

cond-mat.stat-mech↗

arXiv2002

Late stages of coarsening in model C

We present a comprehensive picture of (non-critical) domain growth in model C systems where a non-conserved scalar order parameter is coupled to a conserved concentration field. For quenches into the region where the ordered and disordered phases coexist, we confirm earlier partial numerical results and find a growth exponent $z=3$. For quenches into the ordered region, we confirm the theoretical prediction $z=2$. Finally we discuss the implications of our results for domain growth in the microcanonical $ϕ^4$-model and we offer some criticism of the work of Somoza and Sagui on the morphology and wetting properties of domains.

cond-mat.stat-mech↗

arXiv2002

Comment on ``Deterministic equations of motion and phase ordering dynamics''

Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $ϕ^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng only observed transient dynamics mostly due to the corrections to scaling introduced by lattice effects, and that Ising-like (model A) phase ordering actually takes place at late times. Moreover, we argue that energy conservation manifests itself in different corrections to scaling.

cond-mat.stat-mech↗

arXiv2002

Absorbing Phase Transitions of Branching-Annihilating Random Walks

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of non-trivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.

cond-mat.stat-mech↗

arXiv2001

Critical Coarsening without Surface Tension: the Voter Universality Class

We show that the two-dimensional voter model, usually considered to only be a marginal coarsening system, represents a broad class of models for which phase-ordering takes place without surface tension. We argue that voter-like growth is generically observed at order-disorder nonequilibrium transitions solely driven by interfacial noise between dynamically symmetric absorbing states.

cond-mat.stat-mech↗

arXiv2000

Analytical results for generalized persistence properties of smooth processes

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.

cond-mat.stat-mech↗

arXiv2000

Rare-event induced binding transition of heteropolymers

Sequence heterogeneity broadens the binding transition of a polymer onto a linear or planar substrate. This effect is analyzed in a real-space renormalization group scheme designed to capture the statistics of rare events. In the strongly disordered regime, binding initiates at an exponentially rare set of ``good contacts''. Renormalization of the contact potential yields a Kosterlitz-Thouless type transition in any dimension. This and other predictions are confirmed by extensive numerical simulations of a directed polymer interacting with a columnar defect.

cond-mat.stat-mech↗

arXiv2000

Phase-ordering and persistence: relative effects of space-discretization, chaos, and anisotropy

The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^ıtre & H. Chaté, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface motion. It is shown that ``normal'', curvature-driven-like domain growth is recovered at larger scales than considered before, and that the persistence exponent seems to be universal. Using generalized persistence spectra, the properties of interface motion in this deterministic, chaotic, lattice system are found to ``interpolate'' between those of the two canonical reference systems, the (probabilistic) Ising model, and the (deterministic), space-continuous, time-dependent Ginzburg-Landau equation.

cond-mat.stat-mech↗

arXiv2000

Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''

Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999), cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional systems of sequentially-updated chaotic maps with conserved ``order parameter'' does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e. synchronously-updated coupled map lattices, which are exempt from these crossover effects, and allow for the first precise estimates of persistence exponents in this case.

cond-mat↗

arXiv1998

Comment on ``Nonuniversal Exponents in Interface Growth''

Recently, Newman and Swift[T. J. Newman and M. R. Swift, Phys. Rev. Lett. {\bf 79}, 2261 (1997)] made an interesting suggestion that the strong-coupling exponents of the Kardar-Parisi-Zhang (KPZ) equation may not be universal, but rather depend on the precise form of the noise distribution. We show here that the decrease of surface roughness exponents they observed can be attributed to a percolative effect.

cond-mat.stat-mech↗

arXiv1998

Coiling and Supercoiling of Vortex Filaments in Oscillatory Media

We study the behavior of vortex filaments subject to a uniform density of phase twist in oscillatory media described by the complex Ginzburg-Landau equation. The first instability is a supercritical Hopf bifurcation to stable propagating helical vortices. The secondary instability, also a forward Hopf bifurcation, leads to quasiperiodic supercoiled filaments. The structural changes undergone by these dynamical objects are akin to those of twisted elastic rods, in spite of the presence of the ribbon component of the twist, particular to phase singularities.

chao-dyn↗