Using advanced numerical approaches based on optimization algorithms, much progress
has been achieved for the study of the ground-state and low-temperature behavior of two …

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the
scaling for different coupling distributions. We use recently developed mappings to graph …

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far
from the perturbation location. In this paper, we study the effect of localized perturbations on …

A sampling algorithm is presented that generates spin-glass configurations of the two-
dimensional Edwards-Anderson Ising spin glass at finite temperature with probabilities …

As spin glass materials have extremely slow dynamics, devious numerical methods are
needed to study low-temperature states. A simple and fast optimization version of the …

Using an efficient polynomial-time ground-state algorithm we investigate the Ising spin glass
state at zero temperature in two dimensions. For large sizes, we show that the spin state in a …

By using problem-dependent mappings to computer-science problems and by applying
sophisticated algorithms, one can numerically study some important problems much better …

In the present article, statistical properties regarding the topology and standard percolation
on relative neighborhood graphs (RNGs) for planar sets of points, considering the Euclidean …

The properties of discrete two-dimensional spin glasses depend strongly on the way the
zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal …

We investigated the Loewner evolution driven by the diffusion processes determined by one-
dimensional chaotic maps. Our model works primarily as a deterministic analog of the …