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 that 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 that scale with the system size and have a weight at zero energy P̂v(0) ∼ l−θ ′ with v = l . A low-temperature expansion reveals that, OPF vanish like L−θ , if θ > 0 and remain finite for space-filling lowest excitations with θ = 0. The method can be extended to extract information about the shape and fractal surface of the large-scale lowest excitations. PACS numbers: 7550L, 0550