Scalings of domain wall energies in two dimensional Ising spin glasses

TL;DR

This paper investigates how domain wall energies in 2D Ising spin glasses scale depending on the distribution of random couplings, revealing three classes with different exponents and clarifying the meaning of theta=0.

Contribution

It identifies three distinct classes of scaling behavior for domain wall energies and clarifies the theoretical interpretation of the theta=0 case in 2D spin glasses.

Findings

Three classes of scaling exponents identified (-0.28, 0, 0)

Theta=0 does not imply d=d_l but d <= d_l

Contradicts previous claims about the significance of theta=0

Abstract

We study domain wall energies of two dimensional spin glasses. The scaling of these energies depends on the model's distribution of quenched random couplings, falling into three different classes. The first class is associated with the exponent theta =-0.28, the other two classes have theta = 0, as can be justified theoretically. In contrast to previous claims, we find that theta=0 does not indicate d=d_l but rather d <= d_l, where d_l is the lower critical dimension.