Low-energy excitations in the three-dimensional random-field Ising model (2009)
The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these...
Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition (2009)
We study domain-wall excitations in two-dimensional random-bond Ising spin systems on a square lattice with side length L, subject to two different continuous disorder distributions. In both cases an...
Phase transitions in diluted negative-weight percolation models (2008)
Apolo, L., Melchert, O., Hartmann, A. K.
We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested...
Wolfsheimer, S., Hartmann, A. K.
We study the distribution of the ground-state energy and of the minimum free-energy for RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in the...
Extended scaling for ferromagnetic Ising models with zero-temperature transitions (2008)
Katzgraber, Helmut G., Campbell, I. A., Hartmann, A. K.
We study the second-moment correlation length and the reduced susceptibility of two ferromagnetic Ising models with zero-temperature ordering. By introducing a scaling variable motivated by...
Ground states of 2d +-J Ising spin glasses via stationary Fokker-Planck sampling (2008)
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure...
Helmut G. Katzgraber, M. Körner, F. Liers, A. K. Hartmann
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over...
Replica theory for Levy spin glasses (2008)
Janzen, K., Hartmann, A. K., Engel, A.
Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite...
Negative-weight percolation (2007)
We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative...
Universality in three dimensional random-field ground states (2007)
Physical Journal B, A. K. Hartmann
Abstract. We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three-dimensional diluted...
Ordered phase in the two-dimensional randomly coupled ferromagnet (2007)
True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass stiness...
New extrapolation of overlap distribution in spin glasses (2007)
G. Hed, A. K. Hartmann, E. Domany
PACS. 75.10.Nr – Spin-glass and other random models. PACS. 75.50.Lk – Spin glasses and other random magnets. PACS. 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.). Abstract. –...
RNA Secondary Structures: Complex Statics and Glassy Dynamics (2007)
Wolfsheimer, S., Burghardt, B., Mann, A., Hartmann, A. K.
Models for RNA secondary structures (the topology of folded RNA) without pseudo knots are disordered systems with a complex state-space below a critical temperature. Hence, a complex dynamical...
Droplets in the two-dimensional +-J spin glass: evidence for (non-) universality (2007)
Using mappings to computer-science problems and by applying sophisticated algorithms, one can study numerically many problems much better compared to applying standard approaches like Monte Carlo...
Fractal dimension of domain walls in two-dimensional Ising spin glasses (2007)
We study domain walls in 2d Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of...
Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses (2006)
Amoruso, C., Hartmann, A. K., Hastings, M. B., Moore, M. A.
We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain...
Overcoming system-size limitations in spin glasses (2005)
Katzgraber, Helmut G., Koerner, Mathias, Liers, Frauke, Hartmann, A. K.
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over...
Universality-class dependence of energy distributions in spin glasses (2005)
Katzgraber, Helmut G., Koerner, Mathias, Liers, Frauke, Juenger, Michael, Hartmann, A. K.
We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering...
Reduction of Two-Dimensional Dilute Ising Spin Glasses (2005)
Boettcher, S., Hartmann, A. K.
The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate...
Determining Energy Barriers by Iterated Optimization: The Two-Dimensional Ising Spin Glass (2005)
Amoruso, C., Hartmann, A. K., Moore, M. A.
Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems or proteins. Here we present an approach, which is based on subdividing the...
A new algorithm is presented, which allows to calculate numerically the partition function Z_q of the d-dimensional q-state Potts models for arbitrary real values q>0 at any given temperature T with...
Influence of Collision Cascade Statistics on Pattern Formation of Ion-Sputtered Surfaces (2004)
Feix, M., Hartmann, A. K., Kree, R., Munoz-Garcia, J., Cuerno, R.
Theoretical continuum models that describe the formation of patterns on surfaces of targets undergoing ion-beam sputtering, are based on Sigmund's formula, which describes the spatial distribution of...
Alder, S., Trebst, S., Hartmann, A. K., Troyer, M.
We investigate the performance of flat-histogram methods based on a multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional +/- J spin glass by measuring round-trip times in...
Energy size effects of two-dimensional Ising spin glasses (2004)
Campbell, I. A., Hartmann, A. K., Katzgraber, Helmut G.
We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary...
Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model (2004)
We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an...
Generating droplets in two-dimensional Ising spin glasses by using matching algorithms (2003)
We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to...
Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses (2002)
The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l^{\theta} for large l. It is shown by numerical studies of large droplets in two-dimensional systems that...
Glassy behavior induced by geometrical frustration in a hard-core lattice gas model (2002)
We introduce a hard-core lattice-gas model on generalized Bethe lattices and investigate analytically and numerically its compaction behavior. If compactified slowly, the system undergoes a...
Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass (2002)
We study large-scale, low-energy excitations in the Ising spin glass with Gaussian interactions in two-dimensions at zero temperature, using an optimization algorithm to determine exact ground...
Hiding solutions in random satisfiability problems: A statistical mechanics approach (2001)
Barthel, W., Hartmann, A. K., Leone, M., Ricci-Tersenghi, F., Weigt, M., Zecchina, R.
A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the...
Lower Critical Dimension of Ising Spin Glasses (2001)
Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes...
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations (2001)
Exact ground states of three-dimensional random field Ising magnets (RFIM) with Gaussian distribution of the disorder are calculated using graph-theoretical algorithms. Systems for different...
Ordered phase in the two-dimensional randomly coupled ferromagnet (2000)
Hartmann, A. K., Campbell, I. A.
True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass...
Ordered Phase in the Two-Dimensional Randomly Coupled Ferromagnet (2000)
Introduction For more than two decades the intensive numerical work on the spin glass (SG) problem has been concentrated almost exclusively on the EdwardsAnderson Ising spin glass : Ising spins on a...
Universality in Three Dimensional Random-Field Ground States (1998)
We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three-dimensional diluted Ising...
Cluster-Exact Approximation of Spin Glass Groundstates (1995)
We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not...