Related papers: Frustration and collectivity in spatial networks
This paper examines the impact of static sparsity on the robustness of a trained network to weight perturbations, data corruption, and adversarial examples. We show that, up to a certain sparsity achieved by increasing network width and…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
We study temperature chaos in a two-dimensional Ising spin glass with random quenched bimodal couplings, by an exact computation of the partition functions on large systems. We study two temperature correlators from the total free energy…
We consider the problem of temperature chaos in mean-field spin-glass models defined on random lattices with finite connectivity. By means of an expansion in the order parameter we show that these models display a much stronger chaos effect…
Randomness is known to affect the dynamical behaviour of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero temperature quench of Ising model on two types of random…
We study low-temperature properties of the $XY$ spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters…
We study maximum entropy mechanisms of information exchange between agents modeled by neural networks and the macroscopic states of a society of such agents in a few situations. Mathematical quantification of surprise, distrust of other…
The frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice are investigated taking into account the exchange interactions of atomic spins at the sites of the first (nearest), second (next-nearest) and…
Despite the huge interest in network resilience to stress, most of the studies have concentrated on internal stress damaging network structure (e.g., node removals). Here we study how networks respond to environmental stress deteriorating…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
In the frustrated interaction systems, the nature of ordered configuration can be intrinsically temperature dependent. There, the idea of effective coupling of decorated and frustrated bond plays an important role. The idea of effective…
Frustration, or the competition between interacting components of a network, is often responsible for the complexity of many body systems, from social and neural networks to protein folding and magnetism. In quantum magnetic systems,…
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…
Ground-state and finite-temperature properties of a special class of exactly solvable Ising-Heisenberg planar models are examined using the generalized decoration-iteration and star-triangle mapping transformations. The investigated spin…
We study a slow relaxation process in a frustrated spin system in which a type of screening effect due to a frustrated environment plays an important role. This screening effect is attributed to the highly degenerate configurations of the…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
We study the process of opinion formation in an Ising social network of scientific collaborations. The network is undirected. An Ising spin is associated with each network node being oriented up (red) or down (blue). Certain nodes carry…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…
Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster…