On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field
Probability
2025-11-25 v3 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2509.18066,
title = {On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field},
author = {Heejune Kim},
journal= {arXiv preprint arXiv:2509.18066},
year = {2025}
}
Comments
54 pages, 1 figure. Strengthened Proposition 3.1 to include external fields, revised Proposition 4.1 and the proof of the main theorem accordingly, and made minor revisions and updated acknowledgments