arXiv subjects

Heiko Rieger

Publications and source records attributed to Heiko Rieger.

At least 109 records · Page 6Linked to original sources

arXiv2004

Growing length scales during aging in 2d disordered systems

The non-equilibrium dynamics of three paradigmatic models for two-dimensional systems with quenched disorder is studied with a focus on the existence and analysis of a growing length scale during aging at low temperatures: 1) The random bond Ising ferromagnet, 2) the Edwards-Anderson model for a spin glas, 3) the solid-on-solid model on a disordered substrate (equivalent to the sine-Gordon model with random phase shifts). Interestingly, we find in all three models a length scale that grows algebraically with time (up to the system size in cases 1 and 3, up to the finite equilibrium length in case 2) with a temperature dependent growth exponent. Whereas in cases 1 and 2 this length scale characterizes a coarsening process, it represents in case 3 the growing size of fluctuations during aging.

cond-mat.dis-nn↗

arXiv2004

Collective roughening of elastic lines with hard core interaction in a disordered environment

We investigate by exact optimization methods the roughening of two and three-dimensional systems of elastic lines with point disorder and hard-core repulsion with open boundary conditions. In 2d we find logarithmic behavior whereas in 3d simple random walk-like behavior. The line 'forests' become asymptotically completely entangled as the system height is increased at fixed line density due to increasing line wandering.

cond-mat.dis-nn↗

arXiv2004

Non equilibrium dynamics below the super-roughening transition

The non equilibrium relaxational dynamics of the solid on solid model on a disordered substrate and the Sine Gordon model with random phase shifts is studied numerically. Close to the super-roughening temperature $T_g$ our results for the autocorrelations, spatial correlations and response function as well as for the fluctuation dissipation ratio (FDR) agree well with the prediction of a recent one loop RG calculation, whereas deep in the glassy low temperature phase substantial deviations occur. The change in the low temperature behavior of these quantities compared with the RG predictions is shown to be contained in a change of the functional temperature dependence of the dynamical exponent $z(T)$, which relates the age $t$ of the system with a length scale ${\cal L}(t)$: $z(T)$ changes from a linear $T$-dependence close to $T_g$ to a 1/T-behavior far away from $T_g$. By identifying spatial domains as connected patches of the exactly computable ground states of the system we demonstrate that the growing length scale ${\cal L}(t)$ is the characteristic size of thermally fluctuating clusters around ``typical'' long-lived configurations.

cond-mat.dis-nn↗

arXiv2004

Domain Growth in Random Magnets

We study the kinetics of domain growth in ferromagnets with random exchange interactions. We present detailed Monte Carlo results for the nonconserved random-bond Ising model, which are consistent with power-law growth with a variable exponent. These results are interpreted in the context of disorder barriers with a logarithmic dependence on the domain size. Further, we clarify the implications of logarithmic barriers for both nonconserved and conserved domain growth.

cond-mat.dis-nn↗

arXiv2004

Scaling of the spin stiffness in random spin-1/2 chains : Crossover from pure-metallic behaviour to random singlet-localized regime

In this paper we study the localization transition induced by the disorder in random antiferromagnetic spin-1/2 chains. The results of numerical large scale computations are presented for the XX model using its free fermions representation. The scaling behavior of the spin stiffness is investigated for various disorder strengths. The disorder dependence of the localization length is studied and a comparison between numerical results and bosonization arguments is presented. A non trivial connection between localization effects and the crossover from the pure XX fixed point to the infinite randomness fixed point is pointed out.

cond-mat.str-el↗

arXiv2004

Disorder Induced Phases in Higher Spin Antiferromagnetic Heisenberg Chains

Extensive DMRG calculations for spin S=1/2 and S=3/2 disordered antiferromagnetic Heisenberg chains show a rather distinct behavior in the two cases. While at sufficiently strong disorder both systems are in a random singlet phase, we show that weak disorder is an irrelevant perturbation for the S=3/2 chain, contrary to what expected from a naive application of the Harris criterion. The observed irrelevance is attributed to the presence of a new correlation length due to enhanced end-to-end correlations. This phenomenon is expected to occur for all half-integer S > 1/2 chains. A possible phase diagram of the chain for generic S is also discussed.

cond-mat.stat-mech↗

arXiv2004

Entanglement transition of elastic lines in a strongly disordered environment

We investigate by exact optimization the geometrical properties of three-dimensional elastic line systems with point disorder and hard-core repulsion. The line 'forests' become entangled due to increasing line wandering as the system height is increased, at fixed line density. There is a transition height at which a cluster of pairwise entangled lines spans the system, transverse to average line orientation. Numerical evidence implies that the phenomenon is in the ordinary percolation universality class.

cond-mat.supr-con↗

arXiv2004

Constrained spin dynamics description of random walks on hierarchical scale-free networks

We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule, which allows an analytic approach. We show analytically that the characteristic relaxation time scale grows algebraically with the total number of nodes $N$ as $T \sim N^z$. From a scaling argument, we also show the power-law decay of the autocorrelation function $C_{\bfsigma}(t)\sim t^{-α}$, which is the probability to find the Ising spins in the initial state ${\bfsigma}$ after $t$ time steps, with the state-dependent non-universal exponent $α$. It turns out that the power-law scaling behavior has its origin in an quasi-ultrametric structure of the configuration space.

cond-mat.stat-mech↗

arXiv2004

Random Walks on Complex Networks

We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.

cond-mat.stat-mech↗

arXiv2004

Aging and scaling laws in $β$-hydroquinone-clathrate

The dielectric permittivity of the orientational glass methanol(x=0.73)-$β$-hydroquinone-clathrate has been studied as function of temperature and waiting time using different temperature-time-protocols. We study aging, rejuvenation and memory effects in the glassy phase and discuss similarities and differences to aging in spin-glasses. We argue that the diluted methanol-clathrate, although conceptually close to its magnetic pendants, takes an intermediate character between a true spin-glass and a pure random field system.

cond-mat.dis-nn↗

arXiv2004

Antiferromagnetic Heisenberg chains with bond alternation and quenched disorder

We consider S=1/2 antiferromagnetic Heisenberg chains with alternating bonds and quenched disorder, which represents a theoretical model of the compound CuCl_{2x}Br_{2(1-x)}(γ-{pic})_2. Using a numerical implementation of the strong disorder renormalization group method we study the low-energy properties of the system as a function of the concentration, x, and the type of correlations in the disorder. For perfect correlation of disorder the system is in the random dimer (Griffiths) phase having a concentration dependent dynamical exponent. For weak or vanishing disorder correlations the system is in the random singlet phase, in which the dynamical exponent is formally infinity. We discuss consequences of our results for the experimentally measured low-temperature susceptibility of CuCl_{2x}Br_{2(1-x)}(γ-{pic})_2.

cond-mat.dis-nn↗

arXiv2003

Crossover effects in the random exchange spin-1/2 antiferromagnetic chain

The random antiferromagnetic spin-1/2 XX and XXZ chain is studied numerically for varying strength of the disorder, using exact diagonalization and stochastic series expansion methods. The spin-spin correlation function as well as the stiffness display a clear crossover from the pure behavior (no disorder) to the infinite randomness fixed point or random singlet behavior predicted by the the real space renormalization group. The crossover length scale is shown to diverge as $ξ\sim{\mathcal D}^{-γ}$, where ${\mathcal D}$ is the variance of the random bonds. Our estimates for the exponent $γ$ agrees well within the error bars with the one for the localization length exponent emerging within an analytical bosonization calculation. Exact diagonalization and stochastic series expansion results for the string correlation function are also presented.

cond-mat.str-el↗

arXiv2003

Universal properties of shortest paths in isotropically correlated random potentials

We consider the optimal paths in a $d$-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d=2 and 3. We show that the exponent relation 2nu-omega=1 holds at least in d=2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations.

cond-mat.dis-nn↗

arXiv2002

Critical properties of loop percolation models with optimization constraints

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional bond percolation. In contrast to this an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a new universality class, for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.

cond-mat.dis-nn↗

arXiv2002

Low Temperature Properties of the Random Field Potts Chain

The random field q-States Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q=2), which is also the expectation based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field pertubabtions ('chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is studied for correlated random fields.

cond-mat.dis-nn↗

arXiv2002

Stability of shortest paths in complex networks with random edge weights

We study shortest paths and spanning trees of complex networks with random edge weights. Edges which do not belong to the spanning tree are inactive in a transport process within the network. The introduction of quenched disorder modifies the spanning tree such that some edges are activated and the network diameter is increased. With analytic random-walk mappings and numerical analysis, we find that the spanning tree is unstable to the introduction of disorder and displays a phase-transition-like behavior at zero disorder strength $ε=0$. In the infinite network-size limit ($N\to \infty$), we obtain a continuous transition with the density of activated edges $Φ$ growing like $Φ\sim ε^1$ and with the diameter-expansion coefficient $Υ$ growing like $Υ\sim ε^2$ in the regular network, and first-order transitions with discontinuous jumps in $Φ$ and $Υ$ at $ε=0$ for the small-world (SW) network and the Barabási-Albert scale-free (SF) network. The asymptotic scaling behavior sets in when $N\gg N_c$, where the crossover size scales as $N_c\sim ε^{-2}$ for the regular network, $N_c \sim \exp[αε^{-2}]$ for the SW network, and $N_c \sim \exp[α|\ln ε| ε^{-2}]$ for the SF network. In a transient regime with $N\ll N_c$, there is an infinite-order transition with $Φ\sim Υ\sim \exp[-α/ (ε^2 \ln N)]$ for the SW network and $\sim \exp[ -α/ (ε^2 \ln N/\ln\ln N)]$ for the SF network. It shows that the transport pattern is practically most stable in the SF network.

cond-mat.stat-mech↗

arXiv2002

Numerical study of the disorder-driven roughening transition in an elastic manifold in a periodic potential

We investigate the roughening phase transition of a $(3+1)$-dimensional elastic manifold driven by the completion between a periodic pinning potential and a randomly distributed impurities. The elastic manifold is modeled by a solid-on-solid type interface model, and universal features of the transition from a flat phase (for strong periodic potential) to a rough phase (for strong disorder) are studied at zero temperature using a combinatorial optimization algorithm technique. We find a {\it continuous} transition with a set of numerically estimated critical exponents that we compare with analytic results and those for a periodic elastic medium.

cond-mat.stat-mech↗

arXiv2001

A practical guide to computer simulations

Here practical aspects of conducting research via computer simulations are discussed. The following issues are addressed: software engineering, object-oriented software development, programming style, macros, make files, scripts, libraries, random numbers, testing, debugging, data plotting, curve fitting, finite-size scaling, information retrieval, and preparing presentations. Because of the limited space, usually only short introductions to the specific areas are given and references to more extensive literature are cited. All examples of code are in C/C++.

cond-mat↗