2024/09/03 by R. A. Dumer, Dumer, R. A., Marcelo Magalhães Godoy +1
Computer Science · Mathematics · Physics and Astronomy · #82M31 #Complex Network Analysis Techniques #Energy Efficient Wireless Sensor Networks #FOS: Physical sciences #Graph theory and applications #I.6.6 #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2409.02033
openalex publication_date 2024/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially defined by a regular square lattice and with probability p each site is tested for the possibility of creating a long-range interaction with any other site that has not yet received one. Here, we used the specific case where p=1, meaning that every site in the network has one long-range interaction in addition to the short-range interactions of the regular lattice. These long-range interactions depend on a power-law form, Jij=rij-α, with the geometric distance rij between connected sites i and j. In current two-dimensional model, we found that mean-field critical behavior is observed only at α=0. As α increases, the network size influences the phase transition point of the system, i.e., indicating a crossover behavior. However, given the two-dimensional system, we found the critical behavior of the short-range interaction at α≈2. Thus, the limitation in the number of long-range interactions compared to the globally coupled model, as well as the form of the decay of these interactions, prevented us from finding a regime with finite phase transition points and continuously varying critical exponents in 0<α<2.