The correspondence between long-range and short-range spin glasses

Understand

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance.

• We show that there is a value of sigma of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions.
• We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.