Fractal droplets in two-dimensional spin glass

The two-dimensional Edwards-Anderson model with Gaussian bond distribution is investigated at T = 0 through 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 as theta(D)' = -0.42(4), clearly different from the stiffness exponent for domain wall excitations.