Turing-like patterns in an asymmetric dynamic Ising model

Mélody Merle, Laura Messio, and Julien Mozziconacci
Phys. Rev. E 100, 042111 – Published 8 October 2019

Abstract

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.

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  • Received 26 March 2019
  • Revised 25 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.042111

©2019 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsGeneral PhysicsNetworksStatistical Physics & ThermodynamicsNonlinear DynamicsInterdisciplinary Physics

Authors & Affiliations

Mélody Merle*, Laura Messio, and Julien Mozziconacci

  • Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France

  • *merle@lptmc.jussieu.fr
  • messio@lptmc.jussieu.fr
  • mozziconacci@lptmc.jussieu.fr

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Issue

Vol. 100, Iss. 4 — October 2019

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