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arXiv · 1903.08506

Turing-like patterns in an asymmetric dynamic Ising model

Mélody Merle·Laura Messio·Julien Mozziconacci
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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 rely on infinite-range interactions, this mapping allows us to design an 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 embryo-genesis to build our model, it can be used to study the behavior of other complex systems of interacting agents.

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Mélody Merle, Laura Messio, Julien Mozziconacci. 2019-03-20. Turing-like patterns in an asymmetric dynamic Ising model. https://doi.org/10.1103/physreve.100.042111

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