Phys. Rev. E 77, 061108 (2008) [9 pages]Geometric properties of the three-dimensional Ising and XY modelsReceived 14 March 2008; published 9 June 2008 The fractal structure of high-temperature graphs of the three-dimensional Ising and XY models is investigated by simulating these graphs directly on a cubic lattice and analyzing them with the help of percolation observables. The Ising graphs are shown to percolate right at the Curie critical point. The diverging length scale relevant to the graphs in the vicinity of the percolation threshold is shown to be provided by the spin correlation length. The fractal dimension of the high-temperature graphs at criticality is estimated to be D=1.7349(65) for the Ising and D=1.7626(66) for the XY models. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.77.061108
DOI:
10.1103/PhysRevE.77.061108
PACS:
05.70.Fh, 05.10.−a, 64.60.ah
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