Spherical Spin Glass Model with External Field

We analyze the free energy and overlaps in 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for purpose of understanding transition between this one without field. compute limiting values fluctuations as well three types setting where strength goes to zero dimension variable grows. In particular, we consider field, ground state, a replica. Our methods involve contour integral representation partition function along random matrix techniques. also provide computations matching different scaling regimes. Finally, discuss implications our results susceptibility geometry Gibbs measure. Some findings paper are confirmed rigorously by Landon Sosoe their recent which came out independently simultaneously.