arXiv subjects

Heiko Rieger

Publications and source records attributed to Heiko Rieger.

121 records · Page 7Linked to original sources

arXiv2001

Superconductor-to-Normal Phase Transition in a Vortex Glass Model: Numerical Evidence for a New Percolation Universality Class

The three-dimensional strongly screened vortex-glass model is studied numerically using methods from combinatorial optimization. We focus on the effect of disorder strength on the ground state and found the existence of a disorder-driven normal-to-superconducting phase transition. The transition turns out to be a geometrical phase transition with percolating vortex loops in the ground state configuration. We determine the critical exponents and provide evidence for a new universality class of correlated percolation.

cond-mat.dis-nn↗

arXiv2001

Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential

We study a lattice model of a three-dimensional periodic elastic medium at zero temperature with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in the mixed phase of a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous phase transition from a flat phase to a rough phase. We determine the critical exponents of this roughening transition via finite size scaling obtaining $ν\approx1.3$, $β\approx0.05$, $γ/ν\approx2.9$ and find that they are universal with respect to the periodicity of the lattice potential. The small order parameter exponent is reminiscent of the random field Ising critical behavior in 3$d$.

cond-mat.dis-nn↗

arXiv2001

The Random-bond Potts model in the large-q limit

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.

cond-mat.dis-nn↗

arXiv2000

On the Energy Minima of the SK Model

We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and the quenched energy, looking at the dependence on the starting equilibrium temperature, and performing a systematic analysis of finite size effects.

cond-mat.dis-nn↗

arXiv1999

Dislocations in the ground state of the solid-on-solid model on a disordered substrate

We investigate the effects of topological defects (dislocations) to the ground state of the solid-on-solid (SOS) model on a simple cubic disordered substrate utilizing the min-cost-flow algorithm from combinatorial optimization. The dislocations are found to destabilize and destroy the elastic phase, particularly when the defects are placed only in partially optimized positions. For multi defect pairs their density decreases exponentially with the vortex core energy. Their mean distance has a maximum depending on the vortex core energy and system size, which gives a fractal dimension of $1.27 \pm 0.02$. The maximal mean distances correspond to special vortex core energies for which the scaling behavior of the density of dislocations change from a pure exponential decay to a stretched one. Furthermore, an extra introduced vortex pair is screened due to the disorder-induced defects and its energy is linear in the vortex core energy.

cond-mat.dis-nn↗

arXiv1995

Quantum Spin Glasses in Finite Dimensions

The Ising spin glass model in a transverse field has a zero temperature phase transition driven solely by quantum fluctuations. This quantum phase transition occuring at a critical transverse field strength has attracted much attention recently. We report the progress that has been made via Monte Carlo simulations of the finite dimensional, short range model.

cond-mat↗

arXiv1995

Aging in Disordered Systems

The dynamics of strongly disordered systems becomes extremely slow or glassy at low temperatures, which results in a characteristic aging scenario. This means that the outcome of measurements strongly depends on the history of the system within the glassy phase, even on macroscopic time scale like hours, weeks or years. This area of non-equilibrium dynamics in disordered systems became recently a major focus of research interest, in particular with respect to spin glasses and related systems. Here we give an overview on these activities with a focus on Monte Carlo studies.

cond-mat↗

arXiv1995

Comment on: Dynamic and Static Properties of the Randomly Pinned Flux Array

We reconsider the model of the randomly pinned planar flux array (or the two-dimensional XY-model with random fields and no vortices) in extensive Monte Carlo simulations. We show that contrary to what has been reported recently [Phys.\ Rev.\ Lett.\ {\bf 72}, 4133 (1994)] the disorder-averaged displacement correlation function is different from the pure case for larger values of the disorder. Its slope as a function of the logarithm of disorder is compatible with newer RG-calculation results.

cond-mat↗

arXiv1995

Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?

In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length $ξ$ diverges with an exponent $ν=1.1\pm0.2$ at the critical temperature and that $χ\simξ^{2-η}$ with $η=0.50\pm0.05$ for the connected susceptibility and $χ_{\rm dis}\simξ^{4-\barη}$ with $\barη=1.03\pm0.05$ for the disconnected susceptibility. Together with the amplitude ratio $A=\lim_{T\to T_c}χ_{\rm dis}/χ^2(h_r/T)^2$ being close to one this gives further support for a two exponent scaling scenario implying $\barη=2η$. The magnetization behaves discontinuously at the transition, i.e. $β=0$, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.

cond-mat↗

arXiv1994

Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass

We study the quantum transition at $T=0$ in the spin-$\frac12$ Ising spin--glass in a transverse field in two dimensions. The world line path integral representation of this model corresponds to an effective classical system in (2+1) dimensions, which we study by Monte Carlo simulations. Values of the critical exponents are estimated by a finite-size scaling analysis. We find that the dynamical exponent, $z$, and the correlation length exponent, $ν$, are given by $z = 1.5 \pm 0.05$ and $ν= 1.0 \pm 0.1$. Both the linear and non-linear susceptibility are found to diverge at the critical point.

cond-mat↗

arXiv1994

Thermocycling experiments with the three-dimensional Ising spin glass model

A characteristic feature of the non--equilibrium dynamics of real spin glasses at low temperatures are strong aging effects. These phenomena can be manipulated by changing the external parameters in various ways: a thermo-cycling experiment consists for instance of a short heat pulse during the waiting time, by which the relaxation might be strongly affected. Results of numerical experiments of this kind, performed via Monte Carlo simulations of the three dimensional Ising spin glass model, are presented. The theoretical implications are discussed and the scenario found is compared with the experimental situation.

cond-mat↗

arXiv1993

Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model

The low temperature dynamics of the three dimensional Ising spin glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to decay algebraically and the temperature dependent exponents agree very well with the experimentally determined values. The nonequilibrium autocorrelation function $C(t,t_w)$ shows a crossover at the waiting (or {\em aging}) time $t_w$ from algebraic {\em quasi-equilibrium} decay for times $t$$\ll$$t_w$ to another, faster algebraic decay for $t$$\gg$$t_w$ with an exponent similar to one for the remanent magnetization.

cond-mat↗

arXiv1993

Critical Exponents of the Three Dimensional Random Field Ising Model

The phase transition of the three--dimensional random field Ising model with a discrete ($\pm h$) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the exponents for the magnetization and disconnected susceptibility are consistent with a first order transition, the specific heat appears to saturate indicating no latent heat. Sample to sample fluctuations of the susceptibilty are consistent with the droplet picture for the transition.

cond-mat↗