https://doi.org/10.1140/epjb/e2006-00025-1
Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics
1
Università degli Studi di Parma, Parco Area delle
Scienze 7/a, 43100 Parma, Italy
2
Istituto Nazionale Fisica
della Materia (INFM), UdR PARMA, Parco Area delle Scienze 7/a,
43100 Parma, Italy
Corresponding author: a agliari@fis.unipr.it
Received:
2
September
2005
Revised:
27
October
2005
Published online:
31
January
2006
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.
PACS: 5.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.40.Fb – Random walks and Levy flights / 05.45.Df – Fractals
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006