Ritort, F, Sales, M.
J. Phys. A-Math. Gen. 34 , L333 -L339 (2001).

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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 that measures OFF 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 that scale with the system size and have a weight at zero energy (P) over cap (0) similar to l(-theta ') with nu = l(d). A low-temperature expansion reveals that, OFF 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.