## Abstract

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).

## Keywords

Spin glasses Thouless–Anderson–Palmer equations Cavity equations## Notes

### Acknowledgements

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.

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