Stiffness of the Edwards-Anderson Model in all Dimensions

TL;DR

This paper provides a comprehensive analysis of the stiffness exponent in the Edwards-Anderson spin glass model across all dimensions, proposing that the lower critical dimension is exactly 2.5, which is crucial for understanding spin glass order.

Contribution

It offers the first complete description of the scaling exponent y in all dimensions and establishes that the lower critical dimension is exactly 2.5, combining numerical and theoretical insights.

Findings

Lower critical dimension is exactly 2.5.

Scaling exponent y characterized across all dimensions.

Results constrain theories of spin glass order.

Abstract

A comprehensive description in all dimensions is provided for the scaling exponent $y$ of low-energy excitations in the Ising spin glass introduced by Edwards and Anderson. A combination of extensive numerical as well as theoretical results suggest that its lower critical dimension is {\it exactly} $d_l=5/2$. Such a result would be an essential feature of any complete model of low-temperature spin glass order and imposes a constraint that may help to distinguish between theories.