Related papers: Free energy in the Sherrington-Kirkpatrick model w…
This paper has been withdrawn by the author due to some mistakes
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This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.
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The paper has been withdrawn by authors.
Due to a computational mistake this paper has been withdrawn.
Due to a computational mistake this paper has been withdrawn.
This paper has been withdrawn because we have since found an analytic theory (arXiv:0712.3586) which shows that the dominant contribution to the free energy fluctuations comes from the region t\approx\tau. This regime was unfortunately…
The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica…
In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap.…
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We consider the spherical Sherrington-Kirkpatrick model of spin glass with sparse interaction, where the interactions between most of the pairs of the spin variables are possibly zero. With suitable normalization, we prove that the limiting…
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This paper has been withdrawn by the author.
This paper has been withdrawn by the authors.
This paper has been withdrawn by the author.
There have been comments on this paper which point out unclear motivation and definitions on noncommutative momentum introduced. Therefore, this paper is withdrawn by the author for more clear presentation.
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