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Abstract: The fractal structure of high-temperature graphs of the three-dimensionalIsing and XY models is investigated by simulating these graphs directly on acubic lattice and analyzing them with the help of percolation observables. TheIsing graphs are shown to percolate right at the Curie critical point. Thediverging length scale relevant to the graphs in the vicinity of thepercolation threshold is shown to be provided by the spin correlation length.The fractal dimension of the high-temperature graphs at criticality isestimated to be $D = 1.734965$ for the Ising and $D = 1.762666$ for the XYmodel.



Author: Frank Winter, Wolfhard Janke, Adriaan M. J. Schakel

Source: https://arxiv.org/







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