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

TL;DR

This paper explores the relationship between long-range and short-range spin glasses, identifying specific long-range interaction decay rates that replicate the critical behavior of short-range models in different dimensions.

Contribution

It establishes a correspondence between long-range and short-range spin glasses by analyzing critical behaviors across dimensions and interaction decay rates.

Findings

Critical behavior of long-range models matches 4D short-range models at specific sigma.

Identifies sigma values where long-range models emulate 3D short-range models.

Provides insights into dimensionality effects on spin glass criticality.

Abstract

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.