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arXiv · 2509.18066

On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field

Heejune Kim
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Abstract

We study the phase transition of the Parisi formula for the free energy in the multi-species Sherrington--Kirkpatrick model with a centered Gaussian external field and a positive-semidefinite variance profile matrix. We show that in terms of the strength of the external field and the variance profile, the de Almeida--Thouless surface delineates the boundary between replica symmetric solutions and replica symmetry breaking solutions.

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Heejune Kim. 2025-09-22. On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field. https://arxiv.org/abs/2509.18066

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