Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1999-06-13
J. Stat. Phys. 99, 171 (2000).
Physics
Condensed Matter
Disordered Systems and Neural Networks
42 pages, 3 figures
Scientific paper
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 significance 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 state 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.
Hastings Matthew B.
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