Abstract
Ferromagnetic models are harmonic oscillators in statistical mechanics. Beyond their original scope in tackling phase transition and symmetry breaking in theoretical physics, they are nowadays experiencing a renewal applicative interest as they capture the main features of disparate complex phenomena, whose quantitative investigation in the past were forbidden due to data lacking. After a streamlined introduction to these models, suitably embedded on random graphs, aim of the present paper is to show their importance in a plethora of widespread research fields, so to highlight the unifying framework reached by using statistical mechanics as a tool for their investigation. Specifically we will deal with examples stemmed from sociology, chemistry, cybernetics (electronics) and biology (immunology).
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Notes
- 1.
1 As far as the network remains over-percolated. If the percolation threshold is crossed, the system splits into independent subsystems and the analysis reduces to the sum of the analysis on each subsystem.
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Agliari, E., Barra, A., Galluzzi, A., Pizzoferrato, A., Tantari, D. (2014). Ferromagnetic Models for Cooperative Behavior: Revisiting Universality in Complex Phenomena. In: Celletti, A., Locatelli, U., Ruggeri, T., Strickland, E. (eds) Mathematical Models and Methods for Planet Earth. Springer INdAM Series, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-02657-2_6
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