Fractal Droplets in Two Dimensional Spin Glasses

TL;DR

This paper investigates the fractal nature of droplet excitations in the 2D Edwards-Anderson spin glass model at zero temperature, revealing their fractal dimension and energy scaling behavior through numerical analysis.

Contribution

It provides the first direct numerical evidence of fractal droplet excitations and quantifies their fractal dimension and energy scaling in a 2D spin glass.

Findings

Droplet volume scales as l^D with D ≈ 1.80

Droplet excitation energy scales with an exponent of approximately -0.42

Droplets exhibit fractal geometry distinct from domain walls

Abstract

The two-dimensional Edwards-Anderson model with Gaussian bond distribution is investigated at T=0 with a numerical method. Droplet excitations are directly observed. It turns out that the averaged volume of droplets is proportional to l^D with D = 1.80(2) where l is the spanning length of droplets, revealing their fractal nature. The exponent characterizing the l dependence of the droplet excitation energy is estimated to be -0.42(4), clearly different from the stiffness exponent for domain wall excitations.