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arXiv · 1512.04441

Free energy in the mixed p-spin models with vector spins

Dmitry Panchenko
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Abstract

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which include the Sherrington-Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand's upper bound for the free energy of multiple mixed $p$-spin systems coupled by constraining their overlaps.

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Dmitry Panchenko. 2015-12-14. Free energy in the mixed p-spin models with vector spins. https://arxiv.org/abs/1512.04441

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