Scaling approach to order-parameter fluctuations in disordered frustrated systems

Abstract

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 ${\hat{P}}_v(0)\sim l^{-{\theta }^{\prime }}$ 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.

4 pages, REVTeX. Some modifications; final version accepted for publication in J. Phys. A: Math. and General (Letters)

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Cited by in corpus (4)

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• Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses
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• Order-parameter fluctuations in Ising spin glasses at low temperatures