Interacting spins in random clusters

Thermodynamic properties of finite random clusters of interacting particles are studied with a first principle calculation. The low temperature spin excitations, which are well separated from the high temperature charge excitations, show the characteristic features of a two-level system. The computed Parisi order function has no structure. A simple interacting twolevel system is constructed to model the weakly coupled random clusters in order to study the low temperature spin excitations. The so-obtained magnetic susceptibility exhibits either a broad maximum or a flat plateau before it reaches a finite value at zero temperature.