Cluster approach to spin glasses and the frustrated-percolation problem

Abstract

Exact relations between cluster properties and thermodynamical properties are obtained for an Ising spin glass. The size of the clusters diverges at a temperature higher than the spin-glass transition. The clusters represent fluctuations that interfere with each other giving rise to net correlations of much shorter size than the typical cluster radius. A frustrated-percolation model is introduced that is related to the Ising spin glass as standard percolation is related to the Ising model.