On the energy landscape of the mixed even p-spin model

Wei-Kuo Chen University of Minnesota Madeline Handschy University of Minnesota Gilad Lerman University of Minnesota

Probability mathscidoc:1704.28002

We investigate the energy landscape of the mixed even p-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits exponentially many orthogonal peaks. This improves the results of Chatterjee [20] and Ding-Eldan-Zhai [29], where the former established a logarithmic size of the number of the orthogonal peaks, while the latter proved a polynomial size. Our second main result obtains disorder chaos at zero temperature and at any external field. As a byproduct, this implies that the fluctuation of the maximal energy is superconcentrated when the external field vanishes and obeys a Gaussian limit law when the external field is present.
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  • To appear in Probability Theory and Related Fields. DOI: 10.1007/s00440-017-0773-1
  title={On the energy landscape of the mixed even p-spin model},
  author={Wei-Kuo Chen, Madeline Handschy, and Gilad Lerman},
Wei-Kuo Chen, Madeline Handschy, and Gilad Lerman. On the energy landscape of the mixed even p-spin model. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170418215027360168742.
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