Ground state and spin-class phase of the large-N infinite-range spin glass via supersymmetry

摘要

The large-N infinite-range spin glass is considered, in particular, the number of spin components k needed to form the ground state and the sample-to-sample fluctuations in the Lagrange multiplier field on each site. The physical signifi- cance of k for the correlation Functions is discussed. The difference between the large-N and spherical spin glass is emphasized; a slight difference between the average Lagrange multiplier of the large-N and spherical spin glasses is derived, leading to a slight increase in the energy of the ground stale compared to the naive expectation. Further, there is a change in the low-energy density of excitations in the large-N system, A form of level repulsion, similar to that found in random matrix theory, is found to exist in this system, surviving interactions. Even though the system is an interacting one, a supersymmetric formalism is developed to deal with the problem of averaging over disorder. [References: 12]