Energy landscapes, supergraphs, and "folding funnels" in spin systems

Dynamical connectivity graphs, which describe dynamical transition rates be tween local energy minima of a system, can be displayed against the backgro und of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of th e system in a unified coarse-grained sense. We give examples of the supergr aphs, for several two-dimensional spin and protein-related systems. We demo nstrate that disordered ferromagnets have, supergraphs akin to those of mod el proteins whereas spin glasses behave like random sequences of amino acid s that fold badly. [S1063-651X(99)14808-6].