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Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial…
Matter gets organized at several levels of structural rearrangements. At mesoscopic level one can distinguish between two types of rearrangements, conforming to different close-packing or densification conditions, appearing during different…
Graph clustering discovers groups or communities within networks. Deep learning methods such as autoencoders (AE) extract effective clustering and downstream representations but cannot incorporate rich structural information. While Graph…
We present a comprehensive investigation of the intricate spin dynamics in the non-centrosymmetric compound Sm$_7$Pd$_3$, revealing the coexistence of spin glass, domain glass, and ferromagnetic (FM) behaviors. Magnetic field-dependent…
Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks %, i.e. tensor…
Motivated by recent experimental observations of correlated metallic phases and superconductivity in rhombohedral trilayer graphene (RTG), we perform an unbiased study of electronic ordering instabilities in hole-doped RTG. Specifically, we…
The spin-1/2 Ising-Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry, which enables one to establish a rigorous mapping with the corresponding chain of composite Ising spins tractable within the transfer-matrix…
In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain…
Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing…
Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying…
In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…
Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion…
We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the…
Frustration in the presence of competing interactions is ubiquitous in the physical sciences and is a source of degeneracy and disorder, giving rise to new and interesting physical phenomena. Perhaps nowhere does it occur more simply than…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
Benefiting from the intrinsic supervision information exploitation capability, contrastive learning has achieved promising performance in the field of deep graph clustering recently. However, we observe that two drawbacks of the positive…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
The competition among spin glass (SG), ferromagnetism and Kondo effect has been analysed in a Kondo lattice model where the inter-site coupling $J_{ij}$ between the localized magnetic moments is given by a generalized Mattis model…
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…