Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions

TL;DR

This paper investigates the geometry of low-energy excitations in a one-dimensional Ising spin glass with power-law interactions, revealing complex scaling behavior that supports multiple theoretical models.

Contribution

It provides a detailed analysis of excitation geometries in a finite-temperature spin glass model, incorporating corrections to scaling to compare with existing theories.

Findings

Fractal dimension of excitations surface is either equal to the space dimension or slightly less.

Data cannot be fitted to standard scenarios without corrections to scaling.

Results are consistent with both replica symmetry breaking and droplet/TNT pictures.

Abstract

Results are presented for the geometry of low-energy excitations in the one-dimensional Ising spin chain with power-law interactions, in which the model parameters are chosen to yield a finite spin-glass transition temperature. Both finite-temperature and ground-state studies are carried out. For the range of sizes studied the data cannot be fitted to any of the standard spin-glass scenarios without including corrections to scaling. Incorporating such corrections we find that the fractal dimension of the surface of the excitations, is either equal to the space dimension, consistent with replica symmetry breaking, or very slightly less than it. The latter case is consistent with the droplet and "trivial-nontrivial" (TNT) pictures.