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

E. Agliari (), R. Burioni, D. Cassi and A. Vezzani

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 49, issue 1, 119-125

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Date: 2006
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DOI: 10.1140/epjb/e2006-00025-1

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