Related papers: Frustration of signed networks: How does it affect…

The frustration index is a key measure for analysing signed networks, which has been underused due to its computational complexity. We use an exact optimisation-based method to analyse frustration as a global structural property of signed…

In random networks decorated with Ising spins, an increase of the density of frustrations reduces the transition temperature of the spin-glass ordering. This result is in contradiction to the Bethe theory. Here we investigate if this effect…

Most of the analyses concerning signed networks have focused on the balance theory, hence identifying frustration with undirected, triadic motifs having an odd number of negative edges; much less attention has been paid to their directed…

Computing the frustration index of a signed graph is a key step toward solving problems in many fields including social networks, political science, physics, chemistry, and biology. The frustration index determines the distance of a network…

We study the collective dynamics of oscillator networks with phase-repulsive coupling, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states.…

Attitudinal Network Graphs are signed graphs where edges capture an expressed opinion; two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). A signed graph is called balanced if each of its cycles…

We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged…

A framework for studying the behavior of a classically frustrated signed network in the process of random rewiring is developed. We describe jump probabilities for change in frustration and formulate a theoretical estimate in terms of the…

Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…

We study the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice, taking into account the exchange interactions of atomic spins at the sites of the nearest, next-nearest, and third neighbors. The…

Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this…

For the signed graph associated to a deep neural network, one can compute the frustration level, i.e., test how close or distant the graph is to structural balance. For all the pretrained deep convolutional neural networks we consider, we…

Geometric frustration leads to complex phases of matter with exotic properties. Antiferromagnets on triangular lattices and square ice are two simple models of geometrical frustration. We map their highly degenerated ground-state phase…

Quantum spin chains - the prototypical model for coupled two-level systems - offer a fertile playground both for fundamental and technological applications, ranging from the theory of thermalization to quantum computation. The effects of…

Competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks arXiv:2001.04664 . In this model two different paradigms compete with each other due to the competitive…

The antiferromagnetic Heisenberg model on the two-leg ladder with exchange interactions along the chains, rungs, and diagonals is studied using the Jordan-Wigner transformation and bond-mean-field theory. The inclusion of all three…

We consider the effect of geometric frustration induced by the random distribution of loop lengths in the "fat" graphs of the dynamical triangulations model on coupled antiferromagnets. While the influence of such connectivity disorder is…

In this paper, the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice in an external magnetic field are investigated, taking into account the exchange interactions of atomic spins at the sites of…

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by…

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below…