Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics
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.
Keywords
Cite
@article{arxiv.0810.0216,
title = {Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics},
author = {E. Agliari and R. Burioni and D. Cassi and A. Vezzani},
journal= {arXiv preprint arXiv:0810.0216},
year = {2008}
}