Some properties of the phase diagram for mixed p-spin glasses

@article{Jagannath2015SomePO,
title={Some properties of the phase diagram for mixed p-spin glasses},
author={Aukosh Jagannath and Ian Tobasco},
journal={Probability Theory and Related Fields},
year={2015},
volume={167},
pages={615-672}
}

In this paper we study the Parisi variational problem for mixed p-spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in the first order optimality conditions for the Parisi functional, which is known to be strictly convex. Using this characterization, we study the phase diagram in the temperature-external field plane. We begin by deriving self-consistency conditions for Parisi measures that generalize those of de Almeida and Thouless to… Expand