On Spin Distributions for Generic p-Spin Models
We provide an alternative formula for spin distributions of generic p-spin glass models. As a main application of this expression, we write spin statistics as solutions of partial differential equations and we show that the generic p-spin models satisfy multiscale Thouless–Anderson–Palmer equations as originally predicted in the work of Mézard–Virasoro (J Phys 46(8):1293–1307, 1985).
KeywordsSpin glasses Thouless–Anderson–Palmer equations Cavity equations
The authors would like to thank Louis-Pierre Arguin, Gérard Ben Arous, Dmitry Panchenko, and Ian Tobasco for helpful discussions. This research was conducted while A.A. was supported by NSF DMS-1597864 and NSF Grant CAREER DMS-1653552 and A.J. was supported by NSF OISE-1604232.
- 1.Adler, R., Taylor, J.: Random Fields and Geometry. Springer Monographs in Mathematics. Springer, New York (2007)Google Scholar
- 6.Auffinger, A., Jagannath, A.: Thouless-Anderson-Palmer equations for the generic p-spin glass model, Ann. Probab., to appear. arXiv:1612.06359
- 9.Gikhman, I.I., Skorokhod, A.V.: The Theory of Stochastic Processes. I. Classics in Mathematics. Springer, Berlin (2004). Translated from the Russian by S. Kotz, Reprint of the 1974 editionGoogle Scholar
- 10.Hoover, D.N.: Row-column exchangeability and a generalized model for probability. In: Exchangeability in Probability and Statistics (Rome, 1981), pp. 281–291. North-Holland, Amsterdam-New York (1982)Google Scholar