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By Ball R., Kolokoltsov V., MacKay R.S. (eds.)

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2004. Unifying Concepts in Granular Media and Glasses: From the Statistical Self-organisation and emergence [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] 47 Mechanics of Granular Media to the Theory of Jamming. Elsevier, Amsterdam. , Lippiello, E. and Nicodemi, M. 2006. Universality in solar flare and earthquake occurrence. Physical Review Letters, 96(5), 051102. , Turcottle, D. and Reichenbach, P. 2002. Power-law correlations of landslide areas in central Italy. Earth and Planetary Science Letters, 195, 169–183.

2 Ising model of ferromagnetism Following in the footsteps of Ising and Lenz, we will use the Ising model to study ferromagnetic properties of metals such as iron. We consider a finite square lattice with the property that each site may adopt either an “up” magnetisation or a “down” magnetisation. We will use the notation si = ±1 with i ∈ {1, . . , N } for the spin of site i, adopting the convention that +1 refers to up and −1 to down. 32) i (i,j) where −h i si is intended to represent the effect of an uniform external magnetic field and −J (i,j) si sj measures the energy of the magnetic interactions, which is lowest when all sites are polarised in the same direction.

18). It should be noted that the OFC model intentionally sets the driving δF to be small in order to faithfully mimic a slowly driven many-body system. 3 Empirical data and the OFC model The OFC model shows that a power-law distribution is observed in the energy of earthquakes (see references in [7]). The results are compared to empirical data in Fig. 19. In our example Fi,j represents the total force acted on a single component, but it could potentially represent another physical quantities. 60).

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