2019/03/31 by Mélody Merle, Laura Messio, Julien Mozziconacci
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Artificial intelligence #Biology #Complex system #Computer science #Diffusion #Evolution and Genetic Dynamics #Gene Regulatory Network Analysis #Ising model #Ising spin #Materials science #Nonlinear Dynamics and Pattern Formation #Pattern formation #Physics #Quantum mechanics #Range (aeronautics) #Spin (aerodynamics) #Statistical physics #Thermodynamics #Turing #nlin.AO #nlin.PS #physics.bio-ph
paper · pdf · doi:10.1103/physreve.100.042111
published as Phys. Rev. E 100, 042111 (2019) · 9pages, including 3 pages of appendices, 5 + 2 figures
arxiv created 2019/07/30 · openalex publication_date 2019/10/08 · arxiv updated 2019/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in Ising models always relies on infinite-range interactions, this mapping allows us to design a finite-range-interactions Ising model that can produce patterns observed in reaction-diffusion systems including Turing patterns with a tunable typical length scale. This model has asymmetric interactions and several spin types coexisting at a site. While we use the example of genetic regulation during embryogenesis to build our model, it can be used to study the behavior of other complex systems of interacting agents.