Eur. Phys. J. B 49, 119-125 (2006)
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

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.