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Ground State and Spin Glass Phase of the Large N Infinite Range Spin Glass Via Supersymmetry

M. B. Hastings
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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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M. B. Hastings. 1999-06-13. Ground State and Spin Glass Phase of the Large N Infinite Range Spin Glass Via Supersymmetry. https://doi.org/10.1023/a%3A1018696623673

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