Universal correlations in percolation

Universal formulas for percolation thresholds.

A power law is postulated for both site and bond percolation thresholds. The formula writes pc = p0[(d − 1)(q − 1)]d , where d is the space dimension and q the coordination number. All thresholds up to d → ∞ are found to belong to only three universality classes. For first two classes b = 0 for site dilution while b = a for bond dilution. The last one associated to high dimensions is characteri...

An exact universal amplitude ratio for percolation

The universal amplitude ratio R̃ ξ for percolation in two dimensions is determined exactly using results for the dilute A model in regime 1, by way of a relationship with the q-state Potts model, with q 6 4. The numerical result obtained by Delfino and Cardy by quantum field theory techniques agrees well with the algebraic expression determined here. Percolation is a subject which can be describ...

Universal Velocity Correlations in Disordered and

The response of weakly disordered metallic grains to Aharonov-Bohm ux suggests a rescaling in which statistical correlators become universal. We derive an exact expression for a correlator of level \velocities," and provide numerical evidence which suggests that the universality extends to a wider class of systems and generalizes to arbitrary perturbations providing a new characterization of qu...

Universal spatial correlations in random spinor fields.

We identify universal spatial fluctuations in systems with nontrivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations, and spin currents, both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction. We su...

Smoothed universal correlations in the two - dimensional