Francesco Camilli

An assumption that typically pervades the study of spin glasses is that of independent and identically distributed random variables. In the celebrated Sherrington-Kirkpatrick model this is manifest in the distribution of the quenched disorder. This homogeneity creates a system whose particles are indistinguishable from one another, namely they can be arbitrarily permuted without changing the thermodynamical features of the model. Breaking identicality in the quenched disorder also breaks this global permutation symmetry, with the possibility of leaving it intact only in smaller subgroups of particles involved. The latter procedure leads to the definition of multispecies spin glasses, which are typically harder to analyse. In my talk I will give an overview of the cases we can solve, with a particular focus on multispecies models on the Nishimori Line, that is a particular region of their phase space where they have a clear correspondence with high dimensional inference problems, and concentration of the order parameters holds despite the presence of quenched disorder.