An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences
arXiv:1010.2338 · doi:10.1007/s10955-010-0107-5
Abstract
We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models.