Scaling approach to order-parameter fluctuations in disordered frustrated systems

We present a constructive approach to obtain information about the compactness and shape of large-scale lowest excitations in disordered systems by studying order-parameter fluctuations (OPF) at low temperatures. We show that the parameter $G$ which measures OPF is 1/3 at T=0 provided the ground state is unique and the probability distribution for the lowest excitations is gapless and with finite weight at zero-excitation energy. We then apply zero-temperature scaling to describe the energy and volume spectra of the lowest large-scale excitations which scale with the system size and have a weight at ze ro energy $\hat{P}_v(0)\sim l^{-\theta'}$ with $v=l^d$. A low-temperature expansion reveals that, OPF vanish like $L^{-\theta}$, if $\theta> 0$ and remain finite for space filling lowest excitations with $\theta=0$. The method can be extended to extract information about the shape and fractal surface of the large-scale lowest excitations.