Ground State and Spin-Glass Phase of the Large-N Infinite-Range Spin Glass via Supersymmetry |
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Authors: | M. B. Hastings |
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Affiliation: | (1) Physics Department, Jadwin Hall, Princeton, New Jersey, 08544 |
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Abstract: | 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. |
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Keywords: | spin glass large-N supersymmetry |
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