A conjectured scenario for order-parameter fluctuations in spin glasses

Abstract

We study order-parameter fluctuations (OPF) in disordered systems by considering the behavior of some recently introduced paramaters $G,G_c$ which have proven very useful to locate phase transitions. We prove that both parameters G (for disconnected overlap disorder averages) and $G_c$ (for connected disorder averages) take the respective universal values 1/3 and 13/31 in the $T\to 0$ limit for any {\em finite} volume provided the ground state is {\em unique} and there is no gap in the ground state local-field distributions, conditions which are met in generic spin-glass models with continuous couplings and no gap at zero coupling. This makes $G,G_c$ ideal parameters to locate phase transitions in disordered systems much alike the Binder cumulant is for ordered systems. We check our results by exactly computing OPF in a simple example of uncoupled spins in the presence of random fields and the one-dimensional Ising spin glass. At finite temperatures, we discuss in which conditions the value 1/3 for G may be recovered by conjecturing different scenarios depending on whether OPF are finite or vanish in the infinite-volume limit. In particular, we discuss replica equivalence and its natural consequence ${\lim }_{V\to \infty }G(V,T)=1/3$ when OPF are finite. As an example of a model where OPF vanish and replica equivalence does not give information about G we study the Sherrington-Kirkpatrick spherical spin-glass model by doing numerical simulations for small sizes. Again we find results compatible with G=1/3 in the spin-glass phase.

18 pages, 9 postscript figures

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• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
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Cited by in corpus (7)

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• Numerical study of the SK Model in magnetic field
• Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses
• Statistics of lowest excitations in two dimensional Gaussian spin glasses
• Dependence of RNA secondary structure on the energy model
• Order-parameter fluctuations in Ising spin glasses at low temperatures
• Scaling approach to order-parameter fluctuations in disordered frustrated systems