Crisanti-Sommers formula and simultaneous symmetry breaking in multi-species spherical spin glasses (Q2165918)

In the paper the authors considered the multi-species spherical spin glass model. It is known [\textit{E. Bates} et al., J. Stat. Phys. 174, No. 2, 333--350 (2019; Zbl 1409.60138)] that the limiting free energy of this model is given by a Parisi variational formula. First main result of the paper is about equivalence of the Parisi and Crisanti-Sommers variational formulas. The authors introduced the notions of symmetry breaking and simultaneity. The second main result of the paper is about simultaneous symmetry breaking. Some examples are given to illustrate applications of these results. Proofs of the results are based on identities for Parisi minimizers, and for Crisanti-Sommers minimizers.