A conjectured scenario for order-parameter fluctuations in spin glasses
Ritort, F, Sales, MJ. Phys. A-Math. Gen. 33, 6505 - 6526 (2000)
Times cited: 6
Abstract
We study order-parameter fluctuations (OPF) in disordered systems by considering the behaviour of some recently introduced parameters G, G (c) which have proven very useful in locating 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 —> 0 limit for any finite volume provided the ground state is 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 like the Binder cumulant 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 under 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—>infinity) 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 performing numerical simulations for small sizes. Again we find results compatible with G = 1/3 in the spin-glass phase.