Related papers: Geometrical Frustration and Cluster Spin Glass wit…
In simulations of some infinite range spin glass systems with finite connectivity, it is found that for any resonable computational time, the saturatedenergy per spin that is achieved by a cluster algorithm is lowered in comparison to that…
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…
The Ising model, often seen as the paradigmatic spin model, has been heavily studied for its mathematical description of ferromagnetism in statistical mechanics. We explore a quantum version of this model, the transverse field Ising model,…
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…
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…
Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial…
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect and aging phenomena. There are two…
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…
Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either non-cumulative, which implies an extensive…
We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric…
While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as…
Geometric frustration is a phenomenon in a lattice system where not all interactions can be satisfied, the simplest example being antiferromagnetically coupled spins on a triangular lattice. Frustrated systems are characterized by their…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a…
We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an…
Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A…
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…
We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency…
In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium…