Fluctuations of Correlation Functions in Disordered Systems

The authors study the fluctuations of the two-point correlation function in one-dimensional disordered spin models. These survive even in the thermodynamic limit and, in order to reconstruct their probability distribution from the moments, they study a set of generalised correlation lengths zeta q. These moments may also be calculated within the transfer matrix formalism and provide insight on disorder-induced fluctuations. They show that the zeta q can be computed in Monte Carlo simulations. They discuss the crossover of the correlation decay rate at large distances to dominance by the most probable value given by zeta 0, and the relation with the finite-volume fluctuations of the free energy. Finally they sketch how to extend their arguments to dimensions two and three.