Related papers: Frustration - how it can be measured
As Phil Anderson noted long ago, frustration can be generally defined by measuring the fluctuations in the coupling energy across a plane boundary between two large blocks of material. Since that time, a number of groups have studied the…
Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S.…
The idea of charge frustration is applied to describe the properties of such diverse physical systems as oil-water-surfactant mixtures and metal-ammonia solutions. The minimalist charge-frustrated model possesses one energy scale and two…
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…
After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex models. We show that these systems contain most of the…
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…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
We consider the $\pm J$ Ising model on a cubic lattice with a gauge-invariant disorder distribution. Disorder depends on a parameter $\beta_G$ that plays the role of a chemical potential for the amount of frustration. We study the model at…
In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and…
Three classes of harmonic disorder systems (Lennard-Jones like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the…
Signed networks with positive and negative interaction are widely observed in the real systems. The negative links would induce frustration, then affect global properties of the system. Based on previous studies, frustration of signed…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…
We present a mean field analysis of a fully frustrated Ising spin model on an Ising lattice gas. This is equivalent to a degenerate Blume-Emery-Griffiths model with frustration, which we analyze for different values of the quadrupolar…
Exact ground states are calculated for the Sherrington-Kirkpatrick (SK) spin-glass containing up to N=90 spins. A ground-state energy per spin $e^{\infty}_0 = - 0.7637 \pm 0.0004$ is found from the $N$ dependence of the misfit parameter,…
The concept of geometrical frustration in condensed matter physics refers to the fact that a system has a locally preferred structure with an energy density lower than the infinite ground state. This notion is however often used in a…
The frustrated q-state Potts model is solved exactly on a hierarchical lattice, yielding chaos under rescaling, namely the signature of a spin-glass phase, as previously seen for the Ising (q=2) model. However, the ground-state entropy…
Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the…
We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local…