Related papers: The Random Fuse Network as a Dipolar Magnet
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics…
The ground state critical properties of the Random Field Ising Model (RFIM) on the diamond hierarchical lattice are investigated via a combining method encompassing real space renormalization group and an exact recurrence procedure. The…
We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
Random fields disorder Ising ferromagnets by aligning single spins in the direction of the random field in three space dimensions, or by flipping large ferromagnetic domains at dimensions two and below. While the former requires random…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field…
We study a quasi-statically driven random field Ising model (RFIM) at zero temperature with interactions mediated by the long-range anisotropic Eshelby kernel. Analogously to amorphous solids at their yielding transition, and differently…
The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire is investigated with effective field theory with correlations. Trimodal distribution chosen as a random…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to…
The presence of random fields is well known to destroy ferromagnetic order in Ising systems in two dimensions. When the system is placed in a sufficiently strong external field, however, the size of clusters of like spins diverges. There is…
We analyze the universal features of the critical behaviour of frustrated spin systems with noncollinear order. By means of the field theoretical renormalization group approach, we study the 3d model of a frustrated magnet and obtain…
Extensive Monte Carlo simulations are used to investigate the stability of the ferromagnetic ground state in three-dimensional systems of Ising dipoles with added quenched disorder. These systems model the collective ferromagnetic order…
A random fuse network, or equivalently a two-dimensional spring network with quenched disorder, is subjected to a constant load and thermal noise, and studied by means of numerical simulations. Rupture is thermally activated and the…
We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform…
This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…
The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a…