Geometric Properties of the Three-Dimensional Ising and XY Models

Details Geometric Properties of the Three-Dimensional Ising and XY Models Geometric Properties of the Three-Dimensional Ising and XY Models

2008-03-14

arxiv.org/abs/0803.2177v1

Phys. Rev. E 77, 061108 (2008)

Physics

Condensed Matter

Statistical Mechanics

19 pages

Scientific paper

10.1103/PhysRevE.77.061108

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 model.

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