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The Ising ferromagnet in dimension five: link and spin overlaps

In the simple [hyper]cubic five dimension near neighbor interaction Ising ferromagnet, extensive simulation measurements are made of the link overlap and the spin overlap distributions. These "two replica" measurements are standard in the Spin Glass context but are not usually recorded in ferromagnet simulations. The moments and moment ratios of these distributions (the variance, the kurtosis and the skewness) show clear critical behaviors at the known ordering temperature of the ferromagnet. Analogous overlap effects can be expected quite generally in Ising ferromagnets in any dimension. The link overlap results in particular, with peaks at criticality in the kurtosis and the skewness, also have implications for Spin Glasses.