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arXiv · 0810.0216

Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics

E. Agliari·R. Burioni·D. Cassi·A. Vezzani
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Abstract

We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout the sites of the lattice, updating the relevant spins. Since the walker is biased towards borders between clusters, the border-sites are more likely to be updated with respect to a non-diffusive dynamics and therefore, we expect the spin configurations to be affected. In particular, by means of the box-counting technique, we measure the fractal dimension of magnetic patterns emerging on the lattice, as the temperature is varied. Interestingly, our results provide a geometric signature of the phase transition and they also highlight some non-trivial, quantitative differences between the behaviors pertaining to the diffusive and non-diffusive dynamics.

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E. Agliari, R. Burioni, D. Cassi, A. Vezzani. 2008-10-01. Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics. https://doi.org/10.1140/epjb/e2006-00025-1

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