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 (as a closed set) 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.
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van Enter, A.C.D., de Groote, E. An Ultrametric State Space with a Dense Discrete Overlap Distribution: Paperfolding Sequences. J Stat Phys 142, 223–228 (2011). https://doi.org/10.1007/s10955-010-0107-5
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DOI: https://doi.org/10.1007/s10955-010-0107-5