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Unique magnetic transition process demonstrating the effectiveness of bond percolation theory in a quantum magnet.
Nat Commun
November 2024
Department of Materials Science and Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan.
Like the crystallization of water to ice, magnetic transition occurs at a critical temperature after the slowing down of dynamically fluctuating short-range correlated spins. Here, we report a unique type of magnetic transition characterized by a linear increase in the volume fraction of unconventional static short-range-ordered spin clusters, which triggered a transition into a long-range order at a threshold fraction perfectly matching the bond percolation theory in a new quantum antiferromagnet of pseudo-trigonal Cu(OH)Cl. Static short-range order appeared in its Kagome lattice plane below ca.
View Article and Find Full Text PDFPercolation critical exponents in cluster kinetics of pulse-coupled oscillators.
Chaos
March 2023
Department of Physics, Jeonbuk National University, Jeonju 54896, Republic of Korea.
Transient dynamics leading to the synchrony of a type of pulse-coupled oscillators, so-called scrambler oscillators, has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the evolution of the cluster size distribution for general cluster sizes has not been fully understood yet. In this paper, we study the evolution of the cluster size distribution from the perspective of a percolation model by regarding the number of aggregations as the number of attached bonds.
View Article and Find Full Text PDFPercolation in a simple cubic lattice with distortion.
Phys Rev E
September 2022
Department of Physics, University of Gour Banga, Malda - 732103, West Bengal, India.
Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular positions. The amount of distortion is tunable by a parameter called the distortion parameter.
View Article and Find Full Text PDFSite-bond percolation model of epidemic spreading with vaccination in complex networks.
J Math Biol
October 2022
School of Mathematics, North University of China, Taiyuan, 030051, Shanxi, People's Republic of China.
To study disease transmission with vaccination based on the network, we map an SIR model to a site-bond percolation model. In the case where the vaccination probability is zero, this model degenerates into a bond percolation model without the immunization. Using the method of generation functions, we obtain exact theoretical results for the epidemic threshold and the average outbreak size.
View Article and Find Full Text PDFEffect of initial infection size on a network susceptible-infected-recovered model.
Phys Rev E
July 2022
Department of Physics & I3N, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.
We consider the effect of a nonvanishing fraction of initially infected nodes (seeds) on the susceptible-infected-recovered epidemic model on random networks. This is relevant when the number of arriving infected individuals is large, or to the spread of ideas with publicity campaigns. This model is frequently studied by mapping to a bond percolation problem, in which edges are occupied with the probability p of eventual infection along an edge.
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